Urbanization and agricultural productivity: some lessons from European cities

Urbanization and agricultural productivity: some lessons from European cities Abstract This article evaluates the effect of increasing urbanization on agricultural productivity at the rural-urban fringe for a set of European metropolises. It takes into account changes in total developed area, population density and the level of urban fragmentation associated with urbanization. To cope with endogeneity issues related to urban equilibrium covariates, we set up an instrumental variables strategy based on historical and institutional instruments. Our results indicate that increasing population density increases agricultural productivity at the rural-urban fringe, while increasing urban fragmentation may have a detrimental effect on agricultural productivity at low levels of fragmentation. We use instrumental variable Bayesian model averaging (IVBMA) to address model uncertainty and use an alternative panel dataset to confirm our instrumental strategy. Our results are robust to alternative model specifications and estimation methods. 1. Introduction Although agriculture remains the main user of rural land in many European countries, the amount of farmland has declined, on average, by 4% among the European countries over the last two decades, and this decline is projected to continue (European Environmental Agency, 2006). Most of the farmland loss occurs at the urban fringe on high-quality farmland. Many blame low-density and noncontiguous development, commonly known as urban sprawl, as a primary cause of farmland loss. There are at least three major concerns over the continuing urban sprawl and farmland loss. First, the conversion of the most fertile farmland to development reduces agricultural productivity, which decreases food supply in the short run and threatens food security in the long run. Second, urban sprawl reduces amenities and quality of life in both urban and rural communities. In many places, urban sprawl has encroached into communities to such an extent that the communities themselves have been lost (Wu et al., 2011). Third, urban sprawl may have a detrimental effect on agricultural infrastructure at the urban fringe. With farmland loss, the local agricultural support sector, such as input suppliers or output processors, may lose their businesses because of insufficient demand for their output or insufficient supply of input for their production (Lynch and Carpenter, 2003; Wu et al., 2011). Consequently, agricultural economies may shrink in the short run and become unviable in the long run. Alongside these concerns, urbanization also presents opportunities for agricultural producers at the rural-urban fringe. The emergence of a new customer base provides opportunities for higher value crops. The rapid increase in the number of nurseries, vegetable farms, vineyards, and other high-value crops in many suburban areas show that farmers have remarkable adaptability and capacity to adjust their enterprises to take advantage of the proximity to urban centers.1Lockeretz (1986) examines the characteristics of US counties by their distance to metro areas and finds that counties closer to metro areas tend to have smaller farm sizes, higher intensity, a larger proportion of harvested cropland and a higher standard of living. Larson et al. (2001) report that more than half the value of total US farm production was derived from counties facing urbanization pressure. Lopez et al. (1988) find that when capital gains on land are included, the overall impact of urbanization on profits is positive, although some subsectors of agriculture are adversely affected. The role of agriculture and urbanization has always been at the heart of the debate on sustainable land-use patterns in a modern economy. In this article, we conduct an empirical analysis to evaluate the effect of increasing urbanization on agricultural productivity using data from 282 large urban zones in Europe. We add new insights to the existing literature by analyzing the effect of several dimensions of urbanization on agricultural productivity. These dimensions include changes in total developed area, population density and the level of urban land fragmentation. Our empirical results show that these dimensions affect agricultural productivity in a nonlinear fashion and should be accounted for in urban planning policies. We find that increasing population density increases agricultural productivity while increasing land fragmentation may have a detrimental effect on agricultural productivity at low levels of fragmentation but a positive effect at high levels of fragmentation. Although some studies have examined the effect of urbanization on agriculture in the USA, relatively little research has focused on this issue in Europe, particularly the effect of different dimensions of urbanization on agricultural economies. The next section presents the empirical model and estimation challenges. This is followed by a discussion of data and methodological issues related to the measurement of urbanization in Section 3. Section 4 discusses the estimation strategies, while Section 5 presents the empirical results. Section 6 highlights some policy implications. Section 7 concludes. 2. Empirical model Regional and urban economics literatures reveal that the area, density and patterns of urban development can all affect agricultural productivity at the rural-urban fringe. As a city expands with population growth, a larger customer base will provide opportunities to grow higher-value crops and to market them in new ways (Lockeretz, 1989; Larson et al., 2001). For example, fresh fruits and vegetables can be sold through restaurants and grocery outlets or directly to consumers in farmers markets. In addition, to adapt to rising land values and increasing contact with new residents, farmers may have to change their operations to emphasize higher-value products, more intensive production and enterprises that fit better in an urbanizing environment (Heimlich and Anderson, 2001). Urbanization can also affect agricultural productivity by affecting its critical infrastructure (Lynch and Carpenter, 2003; Wu et al., 2011). For example, with urban development, total cropland will decrease at the rural-urban fringe. This will reduce the demand for agricultural inputs such as fertilizer and seeds. As the demand decreases below a certain threshold, the nearest input supplier may close its business, and the farmer would have to pay more or travel a longer distance for input. Likewise, as the total farmland acreage decreases below a certain threshold, the nearest processor may close, and farmers may have to accept lower output prices or pay additional transport costs for their output. This suggests that even if individual farmers may operate at a constant return to scale, there may be economies of scale at the industry level. Urban development patterns can also affect agricultural productivity. A fragmented development pattern with farms and subdivisions intertwined increases the risk of land use conflicts. Suburban neighbors’ complaints about farm odors, noise and chemical spraying may lead to more stringent land use regulation, which may force farmers to turn to less profitable enterprises (Reynnells, 1987; Van Driesche et al., 1987). Urban smog, theft and vandalism may damage crops. Markets for traditional dairy products or field crops may be reduced as milk-collection routes are curtailed and grain elevators go out of business (Heimlich and Anderson, 2001). To evaluate the effect of area, density and patterns of urban development on agricultural productivity, we estimate the following empirical model using data for a sample of European cities:   πi=f(Ai,Di,Si,Xi;βi)+εi (1) where i is an index of cities, πi is the level of agricultural productivity in city i, Ai is the total developed area, Di is the population density, Si is the degree of urban land fragmentation, Xi is a vector of other covariates affecting agricultural productivity, βi is a vector of parameters and εi is a random error term. When estimating (1), it is important to note that total developed area, population density and urban fragmentation ( Ai, Di,Si) are likely to be endogenous. Standard urban economic theory posits that urbanization increases the demand for urban development, which bids up agricultural land prices. Land conversion expectations and development irreversibility generate a growth premium and an option value, which make up a large portion of farmland values at the rural-urban fringe (Capozza and Helsley, 1990; Plantinga et al., 2002; Cavailhès and Wavresky, 2003; Livanis et al., 2006; Wu and Lin, 2010). In equilibrium, the amounts of land in urban and agricultural uses are determined by equating the rent in urban use to the agricultural rent foregone plus conversion costs and options values (Capozza and Li, 1994; Wu and Chen, 2016). Agricultural land prices capitalize agricultural net returns, growth premium and options values. Changes in agricultural productivity affect land prices and the opportunity cost of land use, which in turn affects the area and pattern of urban development. Thus, efficient estimation of (1) must treat Ai, Di, and Si as potentially endogenous variables. Another major challenge for estimating (1) is model uncertainty. In a closely related paper, Wu et al. (2011) show that in the US net farm income per farmland acre first decreases and then increases with Ai. This suggests that the relationship between farm returns and urbanization may well exhibit nonlinearities. In addition, most of the covariates introduced by Wu et al. (2011) to explain farm returns (e.g. wages in other sectors, median household income, population’s education) were statistically insignificant, although they are theoretically relevant. We thus face uncertainty about the specification of the model. Before presenting the methods used to address these econometric challenges, we first discuss the data used to estimate Equation (1). 3. Data Our data sample was obtained by combining various existing data sources. Our starting point was the complete set of 320 cities included in the Urban Audit (UA) database.2 All cities in the database are defined at three scales: The Core City, which encompasses the administrative boundaries of the city; the Large Urban Zone (LUZ), which is an approximation of the functional urban region centered around the Core city; and the Sub-City District, which is a subdivision of the LUZ (EUROSTAT, 2004). We concentrate on LUZs because farmland development is observed around the fringes of cities. Therefore, the boundaries of each LUZ define the spatial units for this study. UA provides rather limited information on land use, with poor coverage for many cities. As an alternative, we use data on Urban Metropolitan Areas (UMZ), compiled by the European Environment Agency (EEA). Derived from Corine Land Cover, UMZ covers the whole EU-27 at a 200 m resolution for those urban areas that are considered contributing to urban tissue and function (Guerois et al., 2012). Geospatial data on agricultural and nonagricultural areas for each city in 2006 is obtained by superimposing the LUZ boundaries on the UMZ spatial data, using a Geographical Information System (GIS). To illustrate the nature of the spatial data, Figure 1 provides maps documenting the urban (artificial) area for four selected cities: Kielce and Radom (Poland), Eindhoven (Netherlands), and Murcia (Spain). For these cities the figure shows their external boundary and the fragments of urban land. Figure 1 View largeDownload slide Illustration of the urban fragments counting. Figure 1 View largeDownload slide Illustration of the urban fragments counting. The UA data are also supplemented by data obtained from the European Observation Network, Territorial Development and Cohesion (ESPON).3 When combined, these data sources provide a set of explanatory variables covering a broad sample of European cities. Direct measures of agricultural productivity are unavailable for our large sample of European cities. We use agricultural value added per unit of agricultural land (AGRIPROX) to approximate agricultural productivity. This proxy provides a good indicator of farming performance in each city. Data on agricultural value added were obtained from ESPON, and the relevant data on agricultural land area for each LUZ were calculated from the UMZ spatial data. We construct variables to measure the amount of urban development, the level of fragmentation and population density. The total artificial area in square kilometers (ARTIFAREA) is considered as a proxy for all urbanized land in each LUZ. These areas were obtained directly from the spatial UMZ data according to Corine Land Cover nomenclature. This simple measure reflects urban land use in a given area without any prejudgment on internal composition or urban morphology (i.e. the scattered nature of the urban area). Fragmentation measures quantify the degree of discontinuity in development. Scattered development leaves nonused spaces in the built-up areas. In its most simple form, fragmentation is measured as the number of urban patches over the total artificial area (Irwin and Bockstael, 2004; Oueslati et al., 2015) or over population (Arribas-bel et al., 2011). Other measures include the mean patch size (Irwin and Bockstael, 2004; Solon 2009) and the degree of openness, measured by the amount of undeveloped land in the area around an average built-up cell (Burchfield et al., 2006). These are relatively similar ways of describing how fragmented or continuous an urban area is. We construct an index, known as patch density, to reflect urban morphology, in particular, the degree of fragmentation of urban area. The index, which is referred to as the fragmentation index and denoted by FRAG, is calculated by FRAG = FRAGMENTS/ARTIFAREA, where FRAGMENTS represents the number of urban fragments (i.e. individual urban patches) within a specific LUZ. We divide FRAGMENTS by the artificial area within each LUZ to correct for the size effect, since we expect that larger urbanized areas will have more fragments. Figure 1 illustrates the calculation of FRAGMENTS for four cities in the sample. We choose to use only this measure of fragmentation because it is a classical measure of fragmentation (Schneider and Woodcock, 2008; Parent et al., 2009) and because it is highly correlated with other shape metrics such as cohesion, division, edge density and aggregation.4 Moreover, patch density is more coherent with our instrumental strategy. Substituting patch density for other measures of urban fragmentation does not change the results presented here. Population density (DENSITY) is calculated by dividing total population by the total artificial area. Total population for each city is obtained from the ESPON database. The ESPON database also provides comprehensive data for each LUZ on Gross Domestic Product (GDP) adjusted for Purchasing Power Standards and total population (POP).5 We use GDP per capita (GDP_CAP) as a proxy for income that influences consumers’ demand for high-value crops. Higher urban income is expected to increase the demand for high-value crops such as flowers, fruits and vegetable, and thus agricultural value added per hectare. To cope with potential endogeneity issues, in all the following we use lagged GDP per capita (in 2000) and treat GDP_CAP as an exogenous covariate. Furthermore, we added a set of climatic and geographic variables to control for farming potential. The climatic variables include the number of rainy days per year (RAIN), the average temperature of the warmest month in a year (TEMPERATURE) and the average sunshine time per day (SUNSHINE). These variables describe the general climate in the LUZ. A terrain variable, median city center altitude above sea level (MEDALT) is included. This variable is a partial indicator of the ruggedness of the LUZ’s terrain which may have an impact on the potential for farming and urban growth. We also include YWHEAT, the average cereal yield in the area, in the base model. Bosker et al. (2013) provide data on slopes and soil quality for most cities in our sample. We use these data as substitute for our MEDALT and YWHEAT variables in several models. This allows us to check for measurement errors in these variables and, eventually, the endogeneity of YWHEAT. We use highway density (HIGHWAY) from the Eurostat regional data set as a proxy for transport costs. Finally, we include a set of amenity variables to control for the effect of urban development features (in addition to density and patterns) on agricultural productivity. The annual average concentration of NO2 (NO2) is used as an indicator of air pollution in the cities. The number of cinema seats (CINEMA) is used as a proxy for the cultural attractiveness of the central city. A vibrant central city with high environmental and social amenities would be expected to discourage decentralization, and thus may affect the demographic characteristics of urban population and their preferences and demand for agricultural products produced locally. The recorded crime (CRIME) from the Urban Audit is used to account for the security situation in the central city. Patacchini and Zenou (2009) show that European cities with more crime sprawl more. It may also be related to flight from blight phenomena where richer families would move to the city outskirts. These families may exert some social pressure on farmers hence increasing their costs. Darly and Torre (2013) give evidence for the Greater Paris region that these conflicts are important, especially in areas where residents convey an important value to farmland amenities. We gathered partial data on 282 European cities. Considering the availability of agricultural value added and the coverage of Corine Land Cover for 2006, we are left with 208 observations.6 Yet, we do not have information on all potential covariates for each city. The list of potential covariates under study, their definition and the number of cities for which they are available are presented in Table 1. Missing data in our sample have nothing to do with either agricultural value added or urbanization, but relate to the ESPON methodology and countries that did not report the data for given cities. We can treat them as missing completely at random and present unbiased estimates. Table 1 Description of variables Variable  Units  Description  Cases  Mean  Std. Dev.  AGRIPROX  €/ha  Agricultural value added per hectare (purchase power parity)  208  6098  11002  W  Dummy  =1 if western European city, 0 otherwise (North taken as the reference)  208  0.38  0.49  S  Dummy  =1 if southern European city, 0 otherwise (North taken as the reference)  208  0.26  0.44  E  Dummy  =1 if eastern European city, 0 otherwise (North taken as the reference)  208  0.30  0.46  SAREA  1000 km2  Surface area of the city  208  2.08  2.09  SAREA_2  —  SAREA squared  208  8.69  25.71  ARTIFAREA  1000 km2  Artificialized surface area of the city  205  0.29  0.36  ARTIFAREA_2  —  ARTIFAREA squared  205  0.21  0.84  POP  10 millions  Total city Population  208  0.10  0.12  POP_2  —  POP squared  208  0.02  0.10  DENSITY  1000 inh/km2  Inhabitants per km2 of ARTIFAREA  205  5.26  3.97  DENSITY_2  —  DENSITY squared  205  43.30  69.79  FRAG  #/km2  Number of fragments per km2 of ARTIFAREA  205  0.40  0.22  FRAG_2  —  FRAG squared  205  0.20  0.22  GDP_CAP  1000 €/capita  GDP per capita in 2000 (purchase power parity)  208  18.55  8.85  GDP_CAP_2  —  GDP_CAP squared  208  421.99  361.74  YWHEAT  kg/ha  100 kg per hectare  208  48.39  18.56  RAIN  #  Number of rainy days in the year  208  150.71  48.92  SUNSHINE  hrs  Average sunshine time per day  176  5.29  1.25  TEMPERATURE  °C  Average temperature of the warmest months in a year  208  21.71  4.06  NO2  µg/m3  Annual average concentration of NO2  166  28.11  10.73  HIGHWAY  km/km2  Length per surface area  208  29.57  30.89  CRIME  #/inh.  Number per 1000 inhabitants  181  83.59  45.59  BURGLARY  #/inh.  Number per 1000 inhabitants  183  2.91  2.52  ACCESSAIR  Index  Normalized to 100 on the EU mean  177  98.28  36.08  ACCESSRAIL  Index  Normalized to 100 on the EU mean  172  94.12  65.47  ACCESSROAD  Index  Normalized to 100 on the EU mean  173  92.77  58.13  CINEMA  #/inh.  Number of cinema seats per 1000 inhabitants  193  17.16  9.52  GREENSPACE  ha  Surface area in hectare  156  41.38  56.94  MEDALT  100 meters  Median city center altitude above sea level  208  1.31  1.39  MEDALT_2  —  MEDALT squared  208  3.64  7.84  Variable  Units  Description  Cases  Mean  Std. Dev.  AGRIPROX  €/ha  Agricultural value added per hectare (purchase power parity)  208  6098  11002  W  Dummy  =1 if western European city, 0 otherwise (North taken as the reference)  208  0.38  0.49  S  Dummy  =1 if southern European city, 0 otherwise (North taken as the reference)  208  0.26  0.44  E  Dummy  =1 if eastern European city, 0 otherwise (North taken as the reference)  208  0.30  0.46  SAREA  1000 km2  Surface area of the city  208  2.08  2.09  SAREA_2  —  SAREA squared  208  8.69  25.71  ARTIFAREA  1000 km2  Artificialized surface area of the city  205  0.29  0.36  ARTIFAREA_2  —  ARTIFAREA squared  205  0.21  0.84  POP  10 millions  Total city Population  208  0.10  0.12  POP_2  —  POP squared  208  0.02  0.10  DENSITY  1000 inh/km2  Inhabitants per km2 of ARTIFAREA  205  5.26  3.97  DENSITY_2  —  DENSITY squared  205  43.30  69.79  FRAG  #/km2  Number of fragments per km2 of ARTIFAREA  205  0.40  0.22  FRAG_2  —  FRAG squared  205  0.20  0.22  GDP_CAP  1000 €/capita  GDP per capita in 2000 (purchase power parity)  208  18.55  8.85  GDP_CAP_2  —  GDP_CAP squared  208  421.99  361.74  YWHEAT  kg/ha  100 kg per hectare  208  48.39  18.56  RAIN  #  Number of rainy days in the year  208  150.71  48.92  SUNSHINE  hrs  Average sunshine time per day  176  5.29  1.25  TEMPERATURE  °C  Average temperature of the warmest months in a year  208  21.71  4.06  NO2  µg/m3  Annual average concentration of NO2  166  28.11  10.73  HIGHWAY  km/km2  Length per surface area  208  29.57  30.89  CRIME  #/inh.  Number per 1000 inhabitants  181  83.59  45.59  BURGLARY  #/inh.  Number per 1000 inhabitants  183  2.91  2.52  ACCESSAIR  Index  Normalized to 100 on the EU mean  177  98.28  36.08  ACCESSRAIL  Index  Normalized to 100 on the EU mean  172  94.12  65.47  ACCESSROAD  Index  Normalized to 100 on the EU mean  173  92.77  58.13  CINEMA  #/inh.  Number of cinema seats per 1000 inhabitants  193  17.16  9.52  GREENSPACE  ha  Surface area in hectare  156  41.38  56.94  MEDALT  100 meters  Median city center altitude above sea level  208  1.31  1.39  MEDALT_2  —  MEDALT squared  208  3.64  7.84  Table 1 Description of variables Variable  Units  Description  Cases  Mean  Std. Dev.  AGRIPROX  €/ha  Agricultural value added per hectare (purchase power parity)  208  6098  11002  W  Dummy  =1 if western European city, 0 otherwise (North taken as the reference)  208  0.38  0.49  S  Dummy  =1 if southern European city, 0 otherwise (North taken as the reference)  208  0.26  0.44  E  Dummy  =1 if eastern European city, 0 otherwise (North taken as the reference)  208  0.30  0.46  SAREA  1000 km2  Surface area of the city  208  2.08  2.09  SAREA_2  —  SAREA squared  208  8.69  25.71  ARTIFAREA  1000 km2  Artificialized surface area of the city  205  0.29  0.36  ARTIFAREA_2  —  ARTIFAREA squared  205  0.21  0.84  POP  10 millions  Total city Population  208  0.10  0.12  POP_2  —  POP squared  208  0.02  0.10  DENSITY  1000 inh/km2  Inhabitants per km2 of ARTIFAREA  205  5.26  3.97  DENSITY_2  —  DENSITY squared  205  43.30  69.79  FRAG  #/km2  Number of fragments per km2 of ARTIFAREA  205  0.40  0.22  FRAG_2  —  FRAG squared  205  0.20  0.22  GDP_CAP  1000 €/capita  GDP per capita in 2000 (purchase power parity)  208  18.55  8.85  GDP_CAP_2  —  GDP_CAP squared  208  421.99  361.74  YWHEAT  kg/ha  100 kg per hectare  208  48.39  18.56  RAIN  #  Number of rainy days in the year  208  150.71  48.92  SUNSHINE  hrs  Average sunshine time per day  176  5.29  1.25  TEMPERATURE  °C  Average temperature of the warmest months in a year  208  21.71  4.06  NO2  µg/m3  Annual average concentration of NO2  166  28.11  10.73  HIGHWAY  km/km2  Length per surface area  208  29.57  30.89  CRIME  #/inh.  Number per 1000 inhabitants  181  83.59  45.59  BURGLARY  #/inh.  Number per 1000 inhabitants  183  2.91  2.52  ACCESSAIR  Index  Normalized to 100 on the EU mean  177  98.28  36.08  ACCESSRAIL  Index  Normalized to 100 on the EU mean  172  94.12  65.47  ACCESSROAD  Index  Normalized to 100 on the EU mean  173  92.77  58.13  CINEMA  #/inh.  Number of cinema seats per 1000 inhabitants  193  17.16  9.52  GREENSPACE  ha  Surface area in hectare  156  41.38  56.94  MEDALT  100 meters  Median city center altitude above sea level  208  1.31  1.39  MEDALT_2  —  MEDALT squared  208  3.64  7.84  Variable  Units  Description  Cases  Mean  Std. Dev.  AGRIPROX  €/ha  Agricultural value added per hectare (purchase power parity)  208  6098  11002  W  Dummy  =1 if western European city, 0 otherwise (North taken as the reference)  208  0.38  0.49  S  Dummy  =1 if southern European city, 0 otherwise (North taken as the reference)  208  0.26  0.44  E  Dummy  =1 if eastern European city, 0 otherwise (North taken as the reference)  208  0.30  0.46  SAREA  1000 km2  Surface area of the city  208  2.08  2.09  SAREA_2  —  SAREA squared  208  8.69  25.71  ARTIFAREA  1000 km2  Artificialized surface area of the city  205  0.29  0.36  ARTIFAREA_2  —  ARTIFAREA squared  205  0.21  0.84  POP  10 millions  Total city Population  208  0.10  0.12  POP_2  —  POP squared  208  0.02  0.10  DENSITY  1000 inh/km2  Inhabitants per km2 of ARTIFAREA  205  5.26  3.97  DENSITY_2  —  DENSITY squared  205  43.30  69.79  FRAG  #/km2  Number of fragments per km2 of ARTIFAREA  205  0.40  0.22  FRAG_2  —  FRAG squared  205  0.20  0.22  GDP_CAP  1000 €/capita  GDP per capita in 2000 (purchase power parity)  208  18.55  8.85  GDP_CAP_2  —  GDP_CAP squared  208  421.99  361.74  YWHEAT  kg/ha  100 kg per hectare  208  48.39  18.56  RAIN  #  Number of rainy days in the year  208  150.71  48.92  SUNSHINE  hrs  Average sunshine time per day  176  5.29  1.25  TEMPERATURE  °C  Average temperature of the warmest months in a year  208  21.71  4.06  NO2  µg/m3  Annual average concentration of NO2  166  28.11  10.73  HIGHWAY  km/km2  Length per surface area  208  29.57  30.89  CRIME  #/inh.  Number per 1000 inhabitants  181  83.59  45.59  BURGLARY  #/inh.  Number per 1000 inhabitants  183  2.91  2.52  ACCESSAIR  Index  Normalized to 100 on the EU mean  177  98.28  36.08  ACCESSRAIL  Index  Normalized to 100 on the EU mean  172  94.12  65.47  ACCESSROAD  Index  Normalized to 100 on the EU mean  173  92.77  58.13  CINEMA  #/inh.  Number of cinema seats per 1000 inhabitants  193  17.16  9.52  GREENSPACE  ha  Surface area in hectare  156  41.38  56.94  MEDALT  100 meters  Median city center altitude above sea level  208  1.31  1.39  MEDALT_2  —  MEDALT squared  208  3.64  7.84  4. Empirical strategy When estimating (1), we control for major confounding factors affecting agricultural productivity, including soil quality, slope, climate and urban features such as average income and amenities. However, there may be potential unobservables correlated with both the urban equilibrium covariates (Ai, Di and Si) and agricultural productivity and it is difficult to have a strong prior on the sign of the bias induced by the potential endogeneity of urban covariates. To gain insights on this issue, we pursue an instrumental variable strategy, complemented by a separate panel data analysis. As reported later in the article, both approaches yield similar conclusions. 4.1. Instrumental variables We collect two sets of institutional and historical instruments thought to be correlated with urban covariates but not with agricultural productivity. Spatial planning policies drive urban development, influencing its density and fragmentation. There is a great deal of variety in spatial planning governance among European countries (Tosics et al., 2010). We build a set of institutional instruments at the country level describing the coordination among the multilevel jurisdictions in charge of spatial planning in different European countries, based on the typology provided by Tosics et al. (2010, Figure 2, p. 40). Their typology encompasses several important dimensions of spatial planning policies such as, inter alia, the prerogatives of different jurisdictional levels (local, regional and national levels), the locus of power (decentralized or centralized), the relative roles of the public and private sectors, the maturity of the spatial planning system and the discrepancies between goals and achievements of those policies. Their typology yields four classes of spatial planning approaches: the ‘regional economic planning approach’ pursuing a large set of goals driven by the central government like in France, the ‘comprehensive integrated approach’ relying on the coordination of national and regional plans such as in Germany, the ‘land use management’ approach with a large role played by local jurisdictions as it is in the UK, and the ‘urbanism’ tradition, encountered in several Mediterranean countries, focusing on the city and its architecture via townscape and building controls.7 Additionally, we build two other variables describing land-use policies from Silva and Acheampong (2014) who survey land-use planning policies in OECD countries. First, we build a dummy for countries in which competences are mainly at the subnational level, versus national or shared between these two levels (Silva and Acheampong, 2014, Table 2, p. 14). We also build a variable describing the level of coordination in planning following two dimensions: verticality (coordination between national and subnational jurisdictions) and horizontality (coordination among sectoral policies). Silva and Acheampong (2014, Table 6, p. 36) identifies four classes of OECD countries where land-use planning is mainly vertical, mainly horizontal, strongly integrated in both dimensions or weakly coordinated in both dimensions. We believe that we can safely put an exclusion restriction on these institutional instruments because they are derived from historical determinants uncorrelated with agricultural productivity. Table 2 Ordinary least squares estimates   [1]  [2]  [3]  [4]  [5]  [6]  SAREA  −0.212***  −0.347***  −0.316***  −0.148**  −0.270***  −0.226***  (0.065)  (0.082)  (0.087)  (0.066)  (0.077)  (0.079)  SAREA_2    0.017***  0.016***    0.012***  0.010***    (0.005)  (0.005)    (0.004)  (0.004)  POP  0.879  −0.713  −1.235  0.882  1.516  0.954  (0.710)  (1.180)  (1.250)  (0.808)  (1.434)  (1.469)  POP_2    0.464  0.772    −1.361  −1.071    (0.786)  (0.798)    (0.990)  (1.008)  DENSITY  0.147***  0.375***    0.232***  0.424***    (0.025)  (0.065)    (0.032)  (0.057)    DENSITY_2    −0.012***      −0.013***      (0.003)      (0.003)    log(DENSITY)      1.051***      1.275***      (0.167)      (0.118)  FRAG  −1.149***  −5.297***  −5.632***  −0.973**  −5.327***  −5.708***  (0.329)  (0.953)  (0.952)  (0.436)  (1.217)  (1.180)  FRAG_2    4.681***  4.845***    5.007***  5.181***    (0.903)  (0.891)    (1.153)  (1.108)  Additional covariates  A  A + B  A + B  A + C  A + B + C  A + B + C  Adjusted-R2  0.539  0.681  0.686  0.630  0.748  0.760  Observations  173  173  173  108  108  108    [1]  [2]  [3]  [4]  [5]  [6]  SAREA  −0.212***  −0.347***  −0.316***  −0.148**  −0.270***  −0.226***  (0.065)  (0.082)  (0.087)  (0.066)  (0.077)  (0.079)  SAREA_2    0.017***  0.016***    0.012***  0.010***    (0.005)  (0.005)    (0.004)  (0.004)  POP  0.879  −0.713  −1.235  0.882  1.516  0.954  (0.710)  (1.180)  (1.250)  (0.808)  (1.434)  (1.469)  POP_2    0.464  0.772    −1.361  −1.071    (0.786)  (0.798)    (0.990)  (1.008)  DENSITY  0.147***  0.375***    0.232***  0.424***    (0.025)  (0.065)    (0.032)  (0.057)    DENSITY_2    −0.012***      −0.013***      (0.003)      (0.003)    log(DENSITY)      1.051***      1.275***      (0.167)      (0.118)  FRAG  −1.149***  −5.297***  −5.632***  −0.973**  −5.327***  −5.708***  (0.329)  (0.953)  (0.952)  (0.436)  (1.217)  (1.180)  FRAG_2    4.681***  4.845***    5.007***  5.181***    (0.903)  (0.891)    (1.153)  (1.108)  Additional covariates  A  A + B  A + B  A + C  A + B + C  A + B + C  Adjusted-R2  0.539  0.681  0.686  0.630  0.748  0.760  Observations  173  173  173  108  108  108  Note: Dependent variable: log(AGRIPROX). Robust standard-errors in parentheses. ***, **, *: significance at the 1%, 5% and 10% levels, respectively. A: a constant, regional dummies (W, S and E), income per inhabitant (GDP_CAP), agricultural productivity determinants (YWHEAT, RAIN, SUNSHINE, TEMPERATURE, MEDALT). B: squared terms on continuous covariates (GDP_CAP, YWHEAT, RAIN, SUNSHINE, TEMPERATURE, MEDALT). C: city amenities (CRIME, BURGLARY, ACCESSRAIL, ACCESSROAD, CINESEATS and GREENSPACE). Table 2 Ordinary least squares estimates   [1]  [2]  [3]  [4]  [5]  [6]  SAREA  −0.212***  −0.347***  −0.316***  −0.148**  −0.270***  −0.226***  (0.065)  (0.082)  (0.087)  (0.066)  (0.077)  (0.079)  SAREA_2    0.017***  0.016***    0.012***  0.010***    (0.005)  (0.005)    (0.004)  (0.004)  POP  0.879  −0.713  −1.235  0.882  1.516  0.954  (0.710)  (1.180)  (1.250)  (0.808)  (1.434)  (1.469)  POP_2    0.464  0.772    −1.361  −1.071    (0.786)  (0.798)    (0.990)  (1.008)  DENSITY  0.147***  0.375***    0.232***  0.424***    (0.025)  (0.065)    (0.032)  (0.057)    DENSITY_2    −0.012***      −0.013***      (0.003)      (0.003)    log(DENSITY)      1.051***      1.275***      (0.167)      (0.118)  FRAG  −1.149***  −5.297***  −5.632***  −0.973**  −5.327***  −5.708***  (0.329)  (0.953)  (0.952)  (0.436)  (1.217)  (1.180)  FRAG_2    4.681***  4.845***    5.007***  5.181***    (0.903)  (0.891)    (1.153)  (1.108)  Additional covariates  A  A + B  A + B  A + C  A + B + C  A + B + C  Adjusted-R2  0.539  0.681  0.686  0.630  0.748  0.760  Observations  173  173  173  108  108  108    [1]  [2]  [3]  [4]  [5]  [6]  SAREA  −0.212***  −0.347***  −0.316***  −0.148**  −0.270***  −0.226***  (0.065)  (0.082)  (0.087)  (0.066)  (0.077)  (0.079)  SAREA_2    0.017***  0.016***    0.012***  0.010***    (0.005)  (0.005)    (0.004)  (0.004)  POP  0.879  −0.713  −1.235  0.882  1.516  0.954  (0.710)  (1.180)  (1.250)  (0.808)  (1.434)  (1.469)  POP_2    0.464  0.772    −1.361  −1.071    (0.786)  (0.798)    (0.990)  (1.008)  DENSITY  0.147***  0.375***    0.232***  0.424***    (0.025)  (0.065)    (0.032)  (0.057)    DENSITY_2    −0.012***      −0.013***      (0.003)      (0.003)    log(DENSITY)      1.051***      1.275***      (0.167)      (0.118)  FRAG  −1.149***  −5.297***  −5.632***  −0.973**  −5.327***  −5.708***  (0.329)  (0.953)  (0.952)  (0.436)  (1.217)  (1.180)  FRAG_2    4.681***  4.845***    5.007***  5.181***    (0.903)  (0.891)    (1.153)  (1.108)  Additional covariates  A  A + B  A + B  A + C  A + B + C  A + B + C  Adjusted-R2  0.539  0.681  0.686  0.630  0.748  0.760  Observations  173  173  173  108  108  108  Note: Dependent variable: log(AGRIPROX). Robust standard-errors in parentheses. ***, **, *: significance at the 1%, 5% and 10% levels, respectively. A: a constant, regional dummies (W, S and E), income per inhabitant (GDP_CAP), agricultural productivity determinants (YWHEAT, RAIN, SUNSHINE, TEMPERATURE, MEDALT). B: squared terms on continuous covariates (GDP_CAP, YWHEAT, RAIN, SUNSHINE, TEMPERATURE, MEDALT). C: city amenities (CRIME, BURGLARY, ACCESSRAIL, ACCESSROAD, CINESEATS and GREENSPACE). We also define a dummy for former communist countries, where both the tradition of planning and the turn to a market economy may have impacted urban development (Musil, 1993; Sailer-Fliege, 1999). Furthermore, we collect data on cities that were strategically bombed during World War II.8 It has been shown that cities suffering from high destruction may recover fully in a quarter century (Davis and Weinstein, 2002; Miguel and Roland, 2011). They are thus unlikely to be correlated with agricultural productivity. However, most cities suffering from strategic bombing during World War II were heavily destroyed and the building stock had to be rebuilt, following modern urbanism patterns, compared with cities that were not bombed. We thus believe these variables to be correlated with our cities descriptors but not with agricultural productivity and are suitable instruments. Our identification strategy also relies on a set of historical variables, known to be related to city growth. First, we aggregate Acemoglu et al. (2005) data using current cities functional area delimitations (see Section 3). These data describe the population of European cities reaching 5000 inhabitants somewhere between 1400 and 1800. A primary source for these data is Bairoch et al. (1988). From these data, we compute the number of cities that reached 5000 inhabitants before 1800 in each Urban Morphological Zones (UMZ), aggregate population in 1400 and 1800, and population growth between these two dates. In parallel, we use data from Bosker et al. (2013) to build a second set of potential historical instruments. Data from Bosker et al. (2013) also rely on Bairoch et al. (1988), however not covering all European countries under scrutiny in our analysis.9 They span a larger time horizon allowing us to collect data on aggregate population in 1000 and 1400, and population growth between these two dates. Finally, we also use Bosker et al. (2013) to code cities that were on a roman commercial route. It may be argued that the historical development of cities is related to local agricultural potential, in which case using past urbanization as an instrument may be problematic because it would be correlated with contemporary agricultural productivity. Nunn and Quian (2011) show that a higher agricultural potential played a role in the development of European cities before 1900. However, this link is debated (Bosker et al., 2013). In our case, we believe that we can safely put an exclusion restriction on our historical variables for the following reasons. First, and foremost, we control for agricultural potential using nonexcluded instruments related to soil quality, climate and terrain slopes. Second, these links are unlikely to hold in the 21st century. Most of cities’ growth in Europe took place during the 20th century (UN, 2009) and there has been an explosion in agricultural productivity after World War II. Following Bairoch (1997), crops yields have been almost constant in Europe throughout 1800–1950 and multiplied by 3 to 6 between 1950 and 1990. For instance, in France, average wheat yields stayed below 2 tons per hectare (t/ha) between 1815 and 1950, then exploded to more than 4 t/ha in 1980 and more than 8 t/ha in 2001 (Bouchet, 2010). Bairoch (1997) labels this period the ‘third agricultural revolution’. The great improvements in mechanization, animal and plant genetics, mineral pesticides and fertilizers, and the development of the agri-food industry after World War II have profoundly changed and redrawn farming throughout Europe. Hence, soil quality, climate and terrain slopes are likely to be the primary determinants of agricultural productivity that affect urbanization in both the remote past and the present. Our control of these primary determinants ensures the validity of our exclusion restrictions. 4.2. Robustness checks Using deep lags to instrument urban equilibrium strengthens our exclusion restrictions but it may also weaken instrumentation (Stock et al., 2002; Combes et al., 2010; Combes et al., 2011). Moreover, using institutional variables at the national level as instruments can only capture the cross-country variation in urbanization features. For these reasons, the strength of our instruments is uncertain. In the next section we will see that, indeed, while urban equilibrium variables in level (population or artificialized area) are well instrumented, partial F-tests for the instrumentation of density and fragmentation generally lie between 5 and 10. To overcome potential weak instruments issues, we conduct four robustness checks. First, we make use of heteroscedasticity related to nonexcluded instruments in the first stage regressions to build additional internal instruments in the way suggested by Lewbel (2012). This heteroscedasticity is particularly important in the density and fragmentation first-stage regressions and this strategy slightly strengthens our instrumental strategy. Second, we estimate the model using instrumental variables estimators less sensitive to weak instruments (Stock et al., 2002; Chao and Swanson, 2005), including the limited information maximum likelihood estimator (LIML) and the generalized method of continuously-updated moments estimator (GMM-CUE; Hansen et al., 1996). Our results are robust to these alternative estimators. Third, we rely on a Bayesian model averaging (hereafter BMA) framework. Rather than choosing a single model, on a goodness-of-fit or information criterion, to represent the knowledge we have on the process under study, BMA proposes to average over a wide range of models weighted by the strength of empirical evidence in favor of each model called posterior probability in a Bayesian framework. Detailed discussions of BMA can be found in Raftery et al. (1997), Hoeting et al. (1999) and Wasserman (2000). Moral-Benito (2015) offers a review of model averaging applied to economics. This framework allows tackling two issues simultaneously: model uncertainty and a potential weak instrument issue. As underlined earlier, we have strong reasons to believe that the effect of urbanization on agricultural productivity is nonlinear. As widely discussed in the literature, urbanization presents both opportunities and challenges to agriculture. The positive effects may dominate the negative effects at some levels of urbanization, but not at others. Previous empirical analysis of US data indicates that the relationship is nonlinear. For example, Wu et al. (2011) find that in the US net farm income per farmland acre first decreases and then increases with total developed area. The BMA is particularly suited for estimation and inference problems when we are uncertain of which model to choose based on strong empirical evidence or theoretical grounds. Aside from potential nonlinearities, model uncertainty arises because we also include a large set of amenity variables that may indirectly affect agricultural productivity through changes in demographics and labor market conditions as suggested by Glaeser et al. (2001), which may in turn affect demand for agricultural goods and capital and labor costs for farmers. In our setting, we address uncertainty in both stages of our instrumental variable strategy using an extension of the BMA approach to IV models: Instrumental Variable Bayesian Model Averaging (IVBMA). Drawing on earlier work by Kleibergen and Zivot (2003), several authors have recently attempted to develop a methodology to simultaneously address model uncertainty and instrumental variable estimation (Karl and Lenkoski, 2012; Koop et al., 2012; Lenkoski et al., 2014). Lenkoski et al. (2014) developed an IVBMA approach using a two-stage extension of the unit information prior, addressing model uncertainty in both stages. The full approach is extensively described in Lenkoski et al. (2014) and Eicher and Kuenzel (2016). Karl and Lenkoski (2012) developed an IVBMA algorithm which nests an MC3 algorithm within a Gibbs sampler allowing for simultaneous selection on both stages of the model. This approach has been used in recent applications to models of growth (Eicher and Kuenzel, 2016) and models of export diversification (Jetter and Ramírez Hassan, 2015). As stressed by Lenkoski et al. (2014), IVBMA has several interesting features, including limiting over identification issues and indicating the strength of covariates in both stages. We show that our core results are robust to these alternative strategies. Fourth, we further assess the robustness of our results using an alternative panel dataset constructed using OECD Territorial Level 3 (TL3) regions statistics for 2000, 2006 and 2012. TL3 regions are the smallest administrative unit available throughout Europe. They are closely similar to NUTS3 regions in the European classification (Eurostat). TL3 regions are administrative areas and not defined on a functional basis. Nevertheless, in most European countries, these regions have been established around a major city. Hence, we expect our main results to hold at this administrative level though they may be less strong due to the fact that the effects of urban structure on agricultural productivity will be partially hidden, at this geographical scale, by other determinants. We identified 310 TL3 regions covering 13 European countries10 in 2000, 2006 and 2012 for which we have data on gross value added (GVA) and employment in the agricultural sector, population and GDP per capita. Using the panel data, we estimate a fixed-effects panel data model similar to (1) including the covariates and their squared terms. The estimated model is:   Yit=αi+γt+βXit+ɛit, (2) where Yit is our proxy for agricultural productivity, either linear and log-transformed; Xit is a vector of covariates including total population in the TL3 region, population density, our proxy for urban land fragmentation,11 and GDP per capita; αi represents the TL3 regions fixed effect; and γt is the time fixed-effect. The inclusion of TL3 regions fixed-effect controls for time invariant unobservables potentially correlated with urbanization. Estimating (2) by OLS yields an unbiased estimate of β under the strict exogeneity assumption covXit,ɛit=0. Again, we are able to show that our core results hold using this completely different approach. 5. Empirical results12 We first report results from the OLS estimation and then turn to our main results using Instrumental Variable (IV) approaches for different sets of instruments. We then test the robustness of our results showing that they hold under different specifications: adding artificial instruments, using alternative estimators, using Instrumental Bayesian Model Averaging (IVBMA) and using an alternative panel data set to estimate a similar fixed effects model. We show that our main results hold in these different settings. Finally, we discuss the relationship between the features of urban development and agricultural productivity implied by the results. 5.1. Results from OLS estimations Before turning to the IV estimation, we explored simple models relating agricultural value added per hectare (AGRIPROX) to covariates of interest such as DENSITY (Dj), FRAG (Sj), SAREA (Aj) and POP. In all these preliminary models, we searched for Box-Cox transformations of AGRIPROX. All cases pointed unambiguously to the logarithmic transformation. Hence, in the following, we consider only log-linear models where log(AGRIPROX) is the dependent variable. In Table 2, Model [1] includes all covariates of interest (SAREA, POP, DENSITY and FRAG) and controls linearly. The effect of DENSITY is positive while the effects of FRAG and SAREA are negative. Model [2] introduces quadratic terms.13 All are significant but POP and POP_2. The insignificance of POP and POP_2 may be due to the fact that the effect of total population is captured by total surface area (SAREA) and population density (DENSITY). Estimates on DENSITY and DENSITY_2 indicate a concave relationship between agricultural productivity and density. This relationship is strictly increasing over almost the entire observed range of DENSITY in our sample. We thus also estimated models with log(DENSITY), which turns out to be our preferred specification (model [3]). Estimates on FRAG and FRAG_2 imply a convex U-shape relationship between land fragmentation and agricultural productivity in our sample of European cities. Table 2 presents results with alternative control variables. The first set of controls (A) includes regional dummies (W, S and E), average income per inhabitant (GDP_CAP) and agricultural productivity determinants (YWHEAT, RAIN, SUNSHINE, TEMPERATURE, MEDALT). The second set of controls (A + B) includes those in the first set as well as the squared terms of all continuous controls. The third set of control (A + C) includes those in first set and some city amenity measures (CRIME, BURGLARY, ACCESSRAIL, ACCESSROAD, CINESEATS and GREENSPACE), and the fourth set of controls (A + B + C) include those included in the second set and the city amenity measures. Results in Table 2 show that our estimates of parameters of interest are robust to changes in controls, at least qualitatively.14 5.2. Results from the IV approaches We now turn to the instrumental variable estimates, which constitute our main results. We use four sets of instruments to identify the effects of urban equilibrium covariates. We instrument SAREA, POP, FRAG, and their squared terms15 and log(DENSITY). Note, however, that we are controlling for strong exogenous factors determining both agricultural and urban rents16 such as farmland quality (YWHEAT), climate (RAIN, SUNSHINE and TEMPERATURE) and terrain features (MEDALT), thus certainly purging a nonnegligible part of potential endogeneity issues.17 To further explore potential bias in our estimates of the urban covariates at the heart of our argument, we propose several IV approaches, which we believe give much support to the results presented in Table 2. Two-stage least squares (2SLS) IV estimates18 using institutional and historical instruments discussed in Section 4.1 are presented in Table 2. Models [1], [2], [3] and [4] rely on the institutional and historical instruments related to spatial planning described earlier, dummies for former communist countries, and World War II strategic bombings. They also make use of Acemoglu et al. (2005) data on urbanization including the number of cities that reached 5000 inhabitants before 1800, aggregate population in the LUZ in 1400, and population growth in the LUZ between 1400 and 1800, along with their squared terms. These models are over-identified (14 instruments). Reduced form regressions confirm the significance of these institutional and historical instruments and the results are consistent with intuition. For instance, former communist countries’ cities tend to be larger, less dense and more fragmented. Cities in countries with stronger national control on planning policies tend to be larger while cities in countries with a regional economic approach to spatial planning policies tend to be more fragmented. Cities in countries where spatial planning relies on a comprehensive integrated approach are denser. A strong degree of vertical and horizontal coordination in spatial planning policies is related to denser cities. Cities with more developed communities in 1800 or larger population in 1400 tend to be larger and less fragmented today. Cities with a larger increase in population between 1400 and 1800 also tend to be less dense and less fragmented today. Overall, first-stage equations adjusted-R2 and partial F-tests corresponding to the excluded instruments suggest that our instruments are not weak. Sargan tests correctly fail to reject our over-identifying exclusion restrictions. Wu–Hausman tests fail to reject differences between OLS and IV. This is partly due to the fact that OLS bias may be small because we control for climate, slopes and soil quality. 5.3. Robustness checks results We also estimate the model using estimators less sensitive to small sample bias and large numbers of instruments (LIML and GMM-CUE). The results are generally robust to the choice of estimators (e.g. model [3]). Model [4] makes use of different instruments less deeply lagged in the past. Instead of using aggregate population in the LUZ in 1400, we use the same measure for 1800. We also skip population growth in the LUZ between 1400 and 1800 for a built-in estimate of density in 1800 constructed by dividing population in 1800 by the number of cities inside the LUZ. We get very similar results. To strengthen our point, we also make use of heteroscedasticity related to nonexcluded instruments in the first-stage regressions to build additional internal instruments in the way suggested by Lewbel (2012). This heteroscedasticity is particularly important in the density and fragmentation first-stage regressions. 2SLS estimates using additional internal instruments are presented in column [5]. Slightly larger first-stage partial F-tests indicate that it moderately strengthens our IV strategy. Model [6] presents results from the same model using GMM-CUE. Models [7] and [8] present similar estimates using our fourth set of instruments. We substitute Acemoglu et al. (2005) data for that of Bosker et al. (2013). We now use population in 1400, population growth between 1000 and 1400 and their squared terms and a Roman road hub dummy as instruments. In these models, we also substitute YWHEAT for their Bosker et al. soil quality variable19 and MEDALT and MEDALT_2 for their terrain ruggedness measures20 and its square. Our IV strategy confirms the key roles of density and fragmentation in explaining agricultural productivity. There is an increasing and concave relationship between agricultural productivity and urban density and a U-shape relationship with urban fragmentation. These results are robust to different IV strategies, estimators and sample sizes. We conduct additional robustness checks of our main results using an IVBMA model (Karl and Lenkoski, 2012; Lenkoski et al., 2014), which addresses model uncertainty at both stages of the IV estimation. IVBMA estimates are reported in Table A4 of the Online Appendix. The posterior probabilities of inclusion of our parameters of interest are high, indicating that there is little uncertainty about their key role in determining agricultural productivity.21 The posterior estimates have the same sign as in the IV models. Regional dummies and SUNSHINE are also included in almost all models. Again, the IVBMA approaches confirm the key roles of density and fragmentation in explaining agricultural productivity. Results from the panel data model are presented in Table 4. Panel A of the table shows the effect of our covariates of interest on GVA per worker (models [1] and [2]) and its logarithm (models [3] and [4]) using alternatively DENSITY and its squared term and log(DENSITY) as explanatory variables. These results confirm that agricultural productivity is increasing and concave with respect to regional density and the U-shape relationship with regional urban fragmentation. However, the statistical significance of the effect of density is sensitive to model specifications.22 Controlling further for total urbanized area does not change the results. In contrast to the cross-sectional model results, population becomes significant in the panel data model, maybe because the panel data model can better capture the effect of population growth on agricultural productivity. Panel B of Table 4 shows the results of the same models using GVA per hectare as the dependent variable. The results are consistent with those of panel A. Altogether, the robustness checks conducted using the panel data set, built independently from our main cross-section data set, reinforce our conclusions on the links between agricultural productivity and urban density and fragmentation. Table 3 Instrumental variables estimates   [1] IV (2SLS)   [2] IV (2SLS)   [3] IV (GMM-CUE)   [4] IV (2SLS)   Variable  Coef.  Std. Err.  Coef.  Std. Err.  Coef.  Std. Err.  Coef.  Std. Err.  SAREA  −0.304  0.304  −0.295**  0.130  −0.131  0.161  −0.244*  0.142  SAREA_2  0.012  0.012  0.011  0.008  0.002  0.009  0.007  0.008  POP  0.295  3.772              POP_2  −0.455  1.899              log(DENSITY)  1.207**  0.465  1.166***  0.275  1.009***  0.268  1.199***  0.241  FRAG  −9.674**  4.521  −9.680***  3.093  −8.998***  3.334  −9.386***  2.878  FRAG_2  9.365**  4.358  9.342***  3.492  8.511**  3.569  8.983***  3.202  Additional covariates  A  A  A  A  Adjusted-R2  0.622  0.632  —  0.642  Observations  154  154  154  154  Instruments  Institutional & historical (1)  Institutional & historical (1)  Institutional & historical (1)  Institutional & historical (2)    Partial F  Adj.-R2  Partial F  Adj.-R2  —  —  Partial F  Adj.-R2  SAREA  29.12***  0.519  29.12***  0.519  —  —  42.24***  0.584  SAREA_2  58.57***  0.280  58.57***  0.280  —  —  30.52***  0.400  POP  59.37***  0.741      —  —      POP_2  189.17***  0.910      —  —      log(DENSITY)  7.52***  0.664  7.52***  0.664  —  —  7.60***  0.663  FRAG  9.27***  0.403  9.27***  0.403  —  —  9.43***  0.415  FRAG_2  5.40***  0.336  5.40***  0.336  —  —  5.48***  0.341  No. of excluded instruments  14  14  14  12  Wu–Hausman test  1.402  2.042*  —  2.302**  Sargan test  17.442**  17.785**  Hansen J-Test: 10.981*  18.637**    [1] IV (2SLS)   [2] IV (2SLS)   [3] IV (GMM-CUE)   [4] IV (2SLS)   Variable  Coef.  Std. Err.  Coef.  Std. Err.  Coef.  Std. Err.  Coef.  Std. Err.  SAREA  −0.304  0.304  −0.295**  0.130  −0.131  0.161  −0.244*  0.142  SAREA_2  0.012  0.012  0.011  0.008  0.002  0.009  0.007  0.008  POP  0.295  3.772              POP_2  −0.455  1.899              log(DENSITY)  1.207**  0.465  1.166***  0.275  1.009***  0.268  1.199***  0.241  FRAG  −9.674**  4.521  −9.680***  3.093  −8.998***  3.334  −9.386***  2.878  FRAG_2  9.365**  4.358  9.342***  3.492  8.511**  3.569  8.983***  3.202  Additional covariates  A  A  A  A  Adjusted-R2  0.622  0.632  —  0.642  Observations  154  154  154  154  Instruments  Institutional & historical (1)  Institutional & historical (1)  Institutional & historical (1)  Institutional & historical (2)    Partial F  Adj.-R2  Partial F  Adj.-R2  —  —  Partial F  Adj.-R2  SAREA  29.12***  0.519  29.12***  0.519  —  —  42.24***  0.584  SAREA_2  58.57***  0.280  58.57***  0.280  —  —  30.52***  0.400  POP  59.37***  0.741      —  —      POP_2  189.17***  0.910      —  —      log(DENSITY)  7.52***  0.664  7.52***  0.664  —  —  7.60***  0.663  FRAG  9.27***  0.403  9.27***  0.403  —  —  9.43***  0.415  FRAG_2  5.40***  0.336  5.40***  0.336  —  —  5.48***  0.341  No. of excluded instruments  14  14  14  12  Wu–Hausman test  1.402  2.042*  —  2.302**  Sargan test  17.442**  17.785**  Hansen J-Test: 10.981*  18.637**    [5] IV (Lewbel-2SLS)   [6] IV (Lewbel-GMM-CUE)   [7] IV (2SLS)   [8] IV (2SLS)   Variable  Coef.  Std. Err.  Coef.  Std. Err.  Coef.  Std. Err.  Coef.  Std. Err.  SAREA  −0.251***  0.072  −0.248**  0.121  0.025  0.141  −0.141  0.107  SAREA_2  0.008**  0.003  −0.001  0.011  0.000  0.006  0.002  0.007  POP          −4.824  3.104      POP_2          2.118  1.688      log(DENSITY)  0.950***  0.266  0.947***  0.272  1.700***  0.325  1.371***  0.255  FRAG  −9.375***  2.655  −9.360***  2.832  −9.882***  2.397  −7.366***  2.201  FRAG_2  8.769***  2.919  8.815***  3.071  8.976***  2.396  7.078***  2.353  Additional covariates  A  A  A  B  Adjusted-R2  0.646    0.657    Observations  154  154  106  106  Instruments  Institutional & historical (3) + artificial instruments  Institutional & historical (3) + artificial instruments  Institutional & historical (4)  Institutional & historical (4)    Partial F  Adj.-R2  —  —  Partial F  Adj.-R2  Partial F  Adj.-R2  SAREA  47.40***  0.720  —  —  21.64***  0.513  21.64***  0.513  SAREA_2  124.62***  0.771  —  —  12.58***  0.215  12.58***  0.215  POP      —  —  34.35***  0.752      POP_2      —  —  333.94***  0.938      log(DENSITY)  7.25***  0.684  —  —  6.89***  0.699  6.89***  0.699  FRAG  8.48***  0.442  —  —  9.83***  0.477  9.83***  0.477  FRAG_2  6.62***  0.372  —  —  6.20***  0.415  6.20***  0.415  No. of excluded instruments  19  19  15  15  Wu–Hausman test  2.74**  —  0.809  0.829  Sargan test  23.07*  Hansen J-Test: 20.12  18.25**  21.66***    [5] IV (Lewbel-2SLS)   [6] IV (Lewbel-GMM-CUE)   [7] IV (2SLS)   [8] IV (2SLS)   Variable  Coef.  Std. Err.  Coef.  Std. Err.  Coef.  Std. Err.  Coef.  Std. Err.  SAREA  −0.251***  0.072  −0.248**  0.121  0.025  0.141  −0.141  0.107  SAREA_2  0.008**  0.003  −0.001  0.011  0.000  0.006  0.002  0.007  POP          −4.824  3.104      POP_2          2.118  1.688      log(DENSITY)  0.950***  0.266  0.947***  0.272  1.700***  0.325  1.371***  0.255  FRAG  −9.375***  2.655  −9.360***  2.832  −9.882***  2.397  −7.366***  2.201  FRAG_2  8.769***  2.919  8.815***  3.071  8.976***  2.396  7.078***  2.353  Additional covariates  A  A  A  B  Adjusted-R2  0.646    0.657    Observations  154  154  106  106  Instruments  Institutional & historical (3) + artificial instruments  Institutional & historical (3) + artificial instruments  Institutional & historical (4)  Institutional & historical (4)    Partial F  Adj.-R2  —  —  Partial F  Adj.-R2  Partial F  Adj.-R2  SAREA  47.40***  0.720  —  —  21.64***  0.513  21.64***  0.513  SAREA_2  124.62***  0.771  —  —  12.58***  0.215  12.58***  0.215  POP      —  —  34.35***  0.752      POP_2      —  —  333.94***  0.938      log(DENSITY)  7.25***  0.684  —  —  6.89***  0.699  6.89***  0.699  FRAG  8.48***  0.442  —  —  9.83***  0.477  9.83***  0.477  FRAG_2  6.62***  0.372  —  —  6.20***  0.415  6.20***  0.415  No. of excluded instruments  19  19  15  15  Wu–Hausman test  2.74**  —  0.809  0.829  Sargan test  23.07*  Hansen J-Test: 20.12  18.25**  21.66***  Note: Dependent variable: log(AGRIPROX). Robust standard-errors in parentheses. ***, **, *: significance at the 1%, 5% and 10% levels, respectively. A: a constant, regional dummies (W, S and E), income per inhabitant (GDP_CAP), agricultural productivity determinants (YWHEAT, RAIN, SUNSHINE, TEMPERATURE, MEDALT) and squared terms on GDP_CAP, SUNSHINE, TEMPERATURE, MEDALT. Institutional & historical (1): using institutional and Acemoglu et al. (for year 1800) instruments described in the text. Institutional & historical (2): using institutional and Acemoglu et al. (for for year 1400) instruments described in the text. Note: Dependent variable: log(AGRIPROX). Robust standard-errors in parentheses. ***, **, *: significance at the 1%, 5% and 10% levels respectively. A: a constant, regional dummies (W, S and E), income per inhabitant (GDP_CAP), agricultural productivity determinants (YWHEAT, RAIN, SUNSHINE, TEMPERATURE, MEDALT) and squared terms on GDP_CAP, SUNSHINE, TEMPERATURE, MEDALT. B: For model [8] YWHEAT, MEDALT and MEDALT_2 are replaced by covariates from Bosker et al. (see text for details). Institutional & historical (3) + artificial instruments: using institutional and Acemoglu et al. (for year 1400) instruments described in the text and Lewbel artificial instruments built on heteroscedasticity in the first stage. Institutional & historical (4): using institutional and Bosker et al. (for year 1400) instruments described in the text. Table 3 Instrumental variables estimates   [1] IV (2SLS)   [2] IV (2SLS)   [3] IV (GMM-CUE)   [4] IV (2SLS)   Variable  Coef.  Std. Err.  Coef.  Std. Err.  Coef.  Std. Err.  Coef.  Std. Err.  SAREA  −0.304  0.304  −0.295**  0.130  −0.131  0.161  −0.244*  0.142  SAREA_2  0.012  0.012  0.011  0.008  0.002  0.009  0.007  0.008  POP  0.295  3.772              POP_2  −0.455  1.899              log(DENSITY)  1.207**  0.465  1.166***  0.275  1.009***  0.268  1.199***  0.241  FRAG  −9.674**  4.521  −9.680***  3.093  −8.998***  3.334  −9.386***  2.878  FRAG_2  9.365**  4.358  9.342***  3.492  8.511**  3.569  8.983***  3.202  Additional covariates  A  A  A  A  Adjusted-R2  0.622  0.632  —  0.642  Observations  154  154  154  154  Instruments  Institutional & historical (1)  Institutional & historical (1)  Institutional & historical (1)  Institutional & historical (2)    Partial F  Adj.-R2  Partial F  Adj.-R2  —  —  Partial F  Adj.-R2  SAREA  29.12***  0.519  29.12***  0.519  —  —  42.24***  0.584  SAREA_2  58.57***  0.280  58.57***  0.280  —  —  30.52***  0.400  POP  59.37***  0.741      —  —      POP_2  189.17***  0.910      —  —      log(DENSITY)  7.52***  0.664  7.52***  0.664  —  —  7.60***  0.663  FRAG  9.27***  0.403  9.27***  0.403  —  —  9.43***  0.415  FRAG_2  5.40***  0.336  5.40***  0.336  —  —  5.48***  0.341  No. of excluded instruments  14  14  14  12  Wu–Hausman test  1.402  2.042*  —  2.302**  Sargan test  17.442**  17.785**  Hansen J-Test: 10.981*  18.637**    [1] IV (2SLS)   [2] IV (2SLS)   [3] IV (GMM-CUE)   [4] IV (2SLS)   Variable  Coef.  Std. Err.  Coef.  Std. Err.  Coef.  Std. Err.  Coef.  Std. Err.  SAREA  −0.304  0.304  −0.295**  0.130  −0.131  0.161  −0.244*  0.142  SAREA_2  0.012  0.012  0.011  0.008  0.002  0.009  0.007  0.008  POP  0.295  3.772              POP_2  −0.455  1.899              log(DENSITY)  1.207**  0.465  1.166***  0.275  1.009***  0.268  1.199***  0.241  FRAG  −9.674**  4.521  −9.680***  3.093  −8.998***  3.334  −9.386***  2.878  FRAG_2  9.365**  4.358  9.342***  3.492  8.511**  3.569  8.983***  3.202  Additional covariates  A  A  A  A  Adjusted-R2  0.622  0.632  —  0.642  Observations  154  154  154  154  Instruments  Institutional & historical (1)  Institutional & historical (1)  Institutional & historical (1)  Institutional & historical (2)    Partial F  Adj.-R2  Partial F  Adj.-R2  —  —  Partial F  Adj.-R2  SAREA  29.12***  0.519  29.12***  0.519  —  —  42.24***  0.584  SAREA_2  58.57***  0.280  58.57***  0.280  —  —  30.52***  0.400  POP  59.37***  0.741      —  —      POP_2  189.17***  0.910      —  —      log(DENSITY)  7.52***  0.664  7.52***  0.664  —  —  7.60***  0.663  FRAG  9.27***  0.403  9.27***  0.403  —  —  9.43***  0.415  FRAG_2  5.40***  0.336  5.40***  0.336  —  —  5.48***  0.341  No. of excluded instruments  14  14  14  12  Wu–Hausman test  1.402  2.042*  —  2.302**  Sargan test  17.442**  17.785**  Hansen J-Test: 10.981*  18.637**    [5] IV (Lewbel-2SLS)   [6] IV (Lewbel-GMM-CUE)   [7] IV (2SLS)   [8] IV (2SLS)   Variable  Coef.  Std. Err.  Coef.  Std. Err.  Coef.  Std. Err.  Coef.  Std. Err.  SAREA  −0.251***  0.072  −0.248**  0.121  0.025  0.141  −0.141  0.107  SAREA_2  0.008**  0.003  −0.001  0.011  0.000  0.006  0.002  0.007  POP          −4.824  3.104      POP_2          2.118  1.688      log(DENSITY)  0.950***  0.266  0.947***  0.272  1.700***  0.325  1.371***  0.255  FRAG  −9.375***  2.655  −9.360***  2.832  −9.882***  2.397  −7.366***  2.201  FRAG_2  8.769***  2.919  8.815***  3.071  8.976***  2.396  7.078***  2.353  Additional covariates  A  A  A  B  Adjusted-R2  0.646    0.657    Observations  154  154  106  106  Instruments  Institutional & historical (3) + artificial instruments  Institutional & historical (3) + artificial instruments  Institutional & historical (4)  Institutional & historical (4)    Partial F  Adj.-R2  —  —  Partial F  Adj.-R2  Partial F  Adj.-R2  SAREA  47.40***  0.720  —  —  21.64***  0.513  21.64***  0.513  SAREA_2  124.62***  0.771  —  —  12.58***  0.215  12.58***  0.215  POP      —  —  34.35***  0.752      POP_2      —  —  333.94***  0.938      log(DENSITY)  7.25***  0.684  —  —  6.89***  0.699  6.89***  0.699  FRAG  8.48***  0.442  —  —  9.83***  0.477  9.83***  0.477  FRAG_2  6.62***  0.372  —  —  6.20***  0.415  6.20***  0.415  No. of excluded instruments  19  19  15  15  Wu–Hausman test  2.74**  —  0.809  0.829  Sargan test  23.07*  Hansen J-Test: 20.12  18.25**  21.66***    [5] IV (Lewbel-2SLS)   [6] IV (Lewbel-GMM-CUE)   [7] IV (2SLS)   [8] IV (2SLS)   Variable  Coef.  Std. Err.  Coef.  Std. Err.  Coef.  Std. Err.  Coef.  Std. Err.  SAREA  −0.251***  0.072  −0.248**  0.121  0.025  0.141  −0.141  0.107  SAREA_2  0.008**  0.003  −0.001  0.011  0.000  0.006  0.002  0.007  POP          −4.824  3.104      POP_2          2.118  1.688      log(DENSITY)  0.950***  0.266  0.947***  0.272  1.700***  0.325  1.371***  0.255  FRAG  −9.375***  2.655  −9.360***  2.832  −9.882***  2.397  −7.366***  2.201  FRAG_2  8.769***  2.919  8.815***  3.071  8.976***  2.396  7.078***  2.353  Additional covariates  A  A  A  B  Adjusted-R2  0.646    0.657    Observations  154  154  106  106  Instruments  Institutional & historical (3) + artificial instruments  Institutional & historical (3) + artificial instruments  Institutional & historical (4)  Institutional & historical (4)    Partial F  Adj.-R2  —  —  Partial F  Adj.-R2  Partial F  Adj.-R2  SAREA  47.40***  0.720  —  —  21.64***  0.513  21.64***  0.513  SAREA_2  124.62***  0.771  —  —  12.58***  0.215  12.58***  0.215  POP      —  —  34.35***  0.752      POP_2      —  —  333.94***  0.938      log(DENSITY)  7.25***  0.684  —  —  6.89***  0.699  6.89***  0.699  FRAG  8.48***  0.442  —  —  9.83***  0.477  9.83***  0.477  FRAG_2  6.62***  0.372  —  —  6.20***  0.415  6.20***  0.415  No. of excluded instruments  19  19  15  15  Wu–Hausman test  2.74**  —  0.809  0.829  Sargan test  23.07*  Hansen J-Test: 20.12  18.25**  21.66***  Note: Dependent variable: log(AGRIPROX). Robust standard-errors in parentheses. ***, **, *: significance at the 1%, 5% and 10% levels, respectively. A: a constant, regional dummies (W, S and E), income per inhabitant (GDP_CAP), agricultural productivity determinants (YWHEAT, RAIN, SUNSHINE, TEMPERATURE, MEDALT) and squared terms on GDP_CAP, SUNSHINE, TEMPERATURE, MEDALT. Institutional & historical (1): using institutional and Acemoglu et al. (for year 1800) instruments described in the text. Institutional & historical (2): using institutional and Acemoglu et al. (for for year 1400) instruments described in the text. Note: Dependent variable: log(AGRIPROX). Robust standard-errors in parentheses. ***, **, *: significance at the 1%, 5% and 10% levels respectively. A: a constant, regional dummies (W, S and E), income per inhabitant (GDP_CAP), agricultural productivity determinants (YWHEAT, RAIN, SUNSHINE, TEMPERATURE, MEDALT) and squared terms on GDP_CAP, SUNSHINE, TEMPERATURE, MEDALT. B: For model [8] YWHEAT, MEDALT and MEDALT_2 are replaced by covariates from Bosker et al. (see text for details). Institutional & historical (3) + artificial instruments: using institutional and Acemoglu et al. (for year 1400) instruments described in the text and Lewbel artificial instruments built on heteroscedasticity in the first stage. Institutional & historical (4): using institutional and Bosker et al. (for year 1400) instruments described in the text. Table 4 Panel data estimates Panel A—dependent variable: GVA per worker     [1] Linear  [2] Linear  [3] Log-linear  [4] Log-linear  POP  −5960.007***  −6523.646***  −0.217***  −0.217***  (2085.482)  (1996.367)  (0.071)  (0.070)  POP_2  180.055**  182.041**  0.006**  0.006**  (88.800)  (80.897)  (0.003)  (0.003)  log(DENSITY)  —  11126.042***  —  0.042    (1926.419)    (0.064)  DENSITY  2697.290  —  0.014  —  (1931.881)    (0.074)    DENSITY _2  268.116  —  0.003  —  (280.009)    (0.011)    FRAG  −10246.459***  −11382.715***  −0.256***  −0.268***  (2626.592)  (2584.500)  (0.082)  (0.081)  FRAG_2  1836.180***  2210.350***  0.058***  0.061***  (612.100)  (594.933)  (0.020)  (0.020)  GDP_CAP  10858.356***  10433.578***  0.647***  0.621***  (3279.907)  (3356.435)  (0.096)  (0.094)  GDP_CAP  −938.586*  −904.933*  −0.075***  −0.072***  (511.803)  (518.286)  (0.014)  (0.014)  Adjusted-R2  0.172  0.168  0.276  0.275  Observations  930  930  930  930    Panel B—dependent variable: GVA per hectare     [5] Linear  [6] Linear  [7] Log-linear  [8] Log-linear    POP  −0.022**  −0.020**  −0.189***  −0.181**  (0.009)  (0.008)  (0.071)  (0.072)  POP_2  0.001  0.001  0.006**  0.006**  (0.001)  (0.001)  (0.003)  (0.003)  log(DENSITY)  —  −0.009  —  −0.052    (0.011)    (0.052)  DENSITY  −0.022  —  −0.056  —  (0.018)    (0.062)    DENSITY _2  0.003  —  0.008  —  (0.003)    (0.009)    FRAG  −0.025*  −0.026**  −0.174**  −0.179**  (0.013)  (0.013)  (0.073)  (0.072)  FRAG_2  0.005  0.006*  0.039**  0.040**  (0.003)  (0.003)  (0.018)  (0.017)  GDP_CAP  0.014  0.013  0.276***  0.261***  (0.018)  (0.018)  (0.088)  (0.087)  GDP_CAP  0.002  0.002  −0.021*  −0.019  (0.004)  (0.004)  (0.013)  (0.012)  Adjusted-R2  0.027  0.026  0.067  0.067  Observations  930  930  930  930  Panel A—dependent variable: GVA per worker     [1] Linear  [2] Linear  [3] Log-linear  [4] Log-linear  POP  −5960.007***  −6523.646***  −0.217***  −0.217***  (2085.482)  (1996.367)  (0.071)  (0.070)  POP_2  180.055**  182.041**  0.006**  0.006**  (88.800)  (80.897)  (0.003)  (0.003)  log(DENSITY)  —  11126.042***  —  0.042    (1926.419)    (0.064)  DENSITY  2697.290  —  0.014  —  (1931.881)    (0.074)    DENSITY _2  268.116  —  0.003  —  (280.009)    (0.011)    FRAG  −10246.459***  −11382.715***  −0.256***  −0.268***  (2626.592)  (2584.500)  (0.082)  (0.081)  FRAG_2  1836.180***  2210.350***  0.058***  0.061***  (612.100)  (594.933)  (0.020)  (0.020)  GDP_CAP  10858.356***  10433.578***  0.647***  0.621***  (3279.907)  (3356.435)  (0.096)  (0.094)  GDP_CAP  −938.586*  −904.933*  −0.075***  −0.072***  (511.803)  (518.286)  (0.014)  (0.014)  Adjusted-R2  0.172  0.168  0.276  0.275  Observations  930  930  930  930    Panel B—dependent variable: GVA per hectare     [5] Linear  [6] Linear  [7] Log-linear  [8] Log-linear    POP  −0.022**  −0.020**  −0.189***  −0.181**  (0.009)  (0.008)  (0.071)  (0.072)  POP_2  0.001  0.001  0.006**  0.006**  (0.001)  (0.001)  (0.003)  (0.003)  log(DENSITY)  —  −0.009  —  −0.052    (0.011)    (0.052)  DENSITY  −0.022  —  −0.056  —  (0.018)    (0.062)    DENSITY _2  0.003  —  0.008  —  (0.003)    (0.009)    FRAG  −0.025*  −0.026**  −0.174**  −0.179**  (0.013)  (0.013)  (0.073)  (0.072)  FRAG_2  0.005  0.006*  0.039**  0.040**  (0.003)  (0.003)  (0.018)  (0.017)  GDP_CAP  0.014  0.013  0.276***  0.261***  (0.018)  (0.018)  (0.088)  (0.087)  GDP_CAP  0.002  0.002  −0.021*  −0.019  (0.004)  (0.004)  (0.013)  (0.012)  Adjusted-R2  0.027  0.026  0.067  0.067  Observations  930  930  930  930  Note: Robust standard errors in parentheses. ***, **, *: significance at the 1%, 5% and 10% levels, respectively. TL3 regions and year fixed-effects are included but not reported here. Table 4 Panel data estimates Panel A—dependent variable: GVA per worker     [1] Linear  [2] Linear  [3] Log-linear  [4] Log-linear  POP  −5960.007***  −6523.646***  −0.217***  −0.217***  (2085.482)  (1996.367)  (0.071)  (0.070)  POP_2  180.055**  182.041**  0.006**  0.006**  (88.800)  (80.897)  (0.003)  (0.003)  log(DENSITY)  —  11126.042***  —  0.042    (1926.419)    (0.064)  DENSITY  2697.290  —  0.014  —  (1931.881)    (0.074)    DENSITY _2  268.116  —  0.003  —  (280.009)    (0.011)    FRAG  −10246.459***  −11382.715***  −0.256***  −0.268***  (2626.592)  (2584.500)  (0.082)  (0.081)  FRAG_2  1836.180***  2210.350***  0.058***  0.061***  (612.100)  (594.933)  (0.020)  (0.020)  GDP_CAP  10858.356***  10433.578***  0.647***  0.621***  (3279.907)  (3356.435)  (0.096)  (0.094)  GDP_CAP  −938.586*  −904.933*  −0.075***  −0.072***  (511.803)  (518.286)  (0.014)  (0.014)  Adjusted-R2  0.172  0.168  0.276  0.275  Observations  930  930  930  930    Panel B—dependent variable: GVA per hectare     [5] Linear  [6] Linear  [7] Log-linear  [8] Log-linear    POP  −0.022**  −0.020**  −0.189***  −0.181**  (0.009)  (0.008)  (0.071)  (0.072)  POP_2  0.001  0.001  0.006**  0.006**  (0.001)  (0.001)  (0.003)  (0.003)  log(DENSITY)  —  −0.009  —  −0.052    (0.011)    (0.052)  DENSITY  −0.022  —  −0.056  —  (0.018)    (0.062)    DENSITY _2  0.003  —  0.008  —  (0.003)    (0.009)    FRAG  −0.025*  −0.026**  −0.174**  −0.179**  (0.013)  (0.013)  (0.073)  (0.072)  FRAG_2  0.005  0.006*  0.039**  0.040**  (0.003)  (0.003)  (0.018)  (0.017)  GDP_CAP  0.014  0.013  0.276***  0.261***  (0.018)  (0.018)  (0.088)  (0.087)  GDP_CAP  0.002  0.002  −0.021*  −0.019  (0.004)  (0.004)  (0.013)  (0.012)  Adjusted-R2  0.027  0.026  0.067  0.067  Observations  930  930  930  930  Panel A—dependent variable: GVA per worker     [1] Linear  [2] Linear  [3] Log-linear  [4] Log-linear  POP  −5960.007***  −6523.646***  −0.217***  −0.217***  (2085.482)  (1996.367)  (0.071)  (0.070)  POP_2  180.055**  182.041**  0.006**  0.006**  (88.800)  (80.897)  (0.003)  (0.003)  log(DENSITY)  —  11126.042***  —  0.042    (1926.419)    (0.064)  DENSITY  2697.290  —  0.014  —  (1931.881)    (0.074)    DENSITY _2  268.116  —  0.003  —  (280.009)    (0.011)    FRAG  −10246.459***  −11382.715***  −0.256***  −0.268***  (2626.592)  (2584.500)  (0.082)  (0.081)  FRAG_2  1836.180***  2210.350***  0.058***  0.061***  (612.100)  (594.933)  (0.020)  (0.020)  GDP_CAP  10858.356***  10433.578***  0.647***  0.621***  (3279.907)  (3356.435)  (0.096)  (0.094)  GDP_CAP  −938.586*  −904.933*  −0.075***  −0.072***  (511.803)  (518.286)  (0.014)  (0.014)  Adjusted-R2  0.172  0.168  0.276  0.275  Observations  930  930  930  930    Panel B—dependent variable: GVA per hectare     [5] Linear  [6] Linear  [7] Log-linear  [8] Log-linear    POP  −0.022**  −0.020**  −0.189***  −0.181**  (0.009)  (0.008)  (0.071)  (0.072)  POP_2  0.001  0.001  0.006**  0.006**  (0.001)  (0.001)  (0.003)  (0.003)  log(DENSITY)  —  −0.009  —  −0.052    (0.011)    (0.052)  DENSITY  −0.022  —  −0.056  —  (0.018)    (0.062)    DENSITY _2  0.003  —  0.008  —  (0.003)    (0.009)    FRAG  −0.025*  −0.026**  −0.174**  −0.179**  (0.013)  (0.013)  (0.073)  (0.072)  FRAG_2  0.005  0.006*  0.039**  0.040**  (0.003)  (0.003)  (0.018)  (0.017)  GDP_CAP  0.014  0.013  0.276***  0.261***  (0.018)  (0.018)  (0.088)  (0.087)  GDP_CAP  0.002  0.002  −0.021*  −0.019  (0.004)  (0.004)  (0.013)  (0.012)  Adjusted-R2  0.027  0.026  0.067  0.067  Observations  930  930  930  930  Note: Robust standard errors in parentheses. ***, **, *: significance at the 1%, 5% and 10% levels, respectively. TL3 regions and year fixed-effects are included but not reported here. 6. Features of urban development and agricultural productivity The estimated models can be used to assess the impact of fragmentation and density on agricultural productivity. Using the estimates presented in this article, we can express agricultural productivity as a function of density and fragmentation:   π^=fDENSITY,FRAG,X¯, (3) where all other covariates are set at their sample mean X¯. Figure 2 presents iso-return curves in the plane of population density and fragmentation. Blue dots in Figure 2 represent cities included in the sample. Panel (a) is established based on model [4] presented in Table 2. Panels (b) and (c) are established based on IV models [1] and [8] in Table 3. Panel (d) represents the panel data model [2] from Table 4.23 For each panel, given the level of fragmentation, the iso-return curves show that agricultural productivity first increase and then decrease as population density increase. For example, in Panel (a) at fragmentation level 0.2, agricultural productivity increase from about $4000 to $11,000 as population density increases from 5000 inhabitants/km2 to 10,000 inhabitants/km2. Agricultural productivity reaches a maximum at approximately 15,000 inhabitants/km2 before decreasing as density increases. This decrease is not robust as described above with only six cities above this threshold. In other panels, based on models including log(DENSITY), increases in population density always leads to higher agricultural productivity. Figure 2 View largeDownload slide Iso-return curves in the plane of densification and fragmentation (OLS and IV models). Figure 2 View largeDownload slide Iso-return curves in the plane of densification and fragmentation (OLS and IV models). Agricultural productivity is especially sensitive to urban population density in highly fragmented urban areas or near compactly developed urban fringes. Is is relatively less sensitive to population density in urban areas with low or moderate fragmentation. The result that increasing population density increases agricultural productivity is consistent with our expectations based on theory. Increasing population density raises the demand for local produce, which will lead to higher prices and more land allocated to the local produce. In addition, because less land will be allocated to producing traded goods, the demand for input for traded goods will decrease, which will lead to a lower input price and higher per-acre profit for traded goods. This suggests that increasing population density will lead to higher per-acre profit for both local produce and trade goods. In contrast, given the population density, the iso-return curves show that agricultural productivity first decreases and then increases as fragmentation increases. The impact of fragmentation on agricultural productivity is reinforced by increasing population density. At low-population density levels, increased fragmentation barely affects agricultural productivity. However, as population density increases, the effect of fragmentation increases. In Panel (b) of Figure 2, holding population density at 10,000 inhabitants/km2, increasing fragmentation from 0.2 to 0.5 decreases agricultural productivity approximately from $12,000 to $5000. Further increase in fragmentation increases agricultural productivity; agricultural productivity increases approximately from $5000 to $10,000 as fragmentation increases from 0.6 to 0.8. The nonlinear relationship between fragmentation and agricultural productivity is also consistent with our expectations based on theory. Urban fragmentation may increase production costs and make it less profitable to switch from traditional crops to high-value crops. As a result, the output prices of high-value crops will be higher, while the input prices will be lower with increasing fragmentation. The effects of fragmentation on input and output prices of traditional crops will be the opposite. Thus, as fragmentation increases, the per-acre profit for high-value crops tends to increase, while the per-acre profits for traditional crops tends to decrease. At lower levels of fragmentation, the effect on traditional crops dominates the effect on high-value crops, leading to lower productivity as fragmentation increases. The opposite may be true at higher levels of fragmentation because more land is devoted to high-value crops with increasing urbanization and the effect on high-value crops may become dominate. 7. Policy implications Our empirical application suggests that, at least in Europe, increasing population density will improve per-hectare agricultural productivity at most urban fringes. Fragmentation also affects agricultural productivity, but in a nonlinear fashion. Increasing fragmentation reduces agricultural productivity initially. But when fragmentation reaches a certain threshold, further increases in fragmentation will increase agricultural productivity. Currently, less than half of European cities have reached this threshold. The nonlinear relationship between fragmentation and agricultural productivity suggests that different policy strategies should be adopted to protect farm income at the fringe of cities with different levels of fragmentation and population densities. Both the population densities and the level of fragmentation vary significantly across European cities.24 Cities in Northern and Western Europe tend to have low population densities and low fragmentation. In contrast, cities in Southern and Eastern Europe are much more heterogeneous in terms of population densities and spatial configurations. Our results suggest that for cities with low population densities and low fragmentation, such as those located in Northern Europe, anti-sprawl policies, for the benefits of farming, should concentrate on both density control and pattern management. In those cities, policies that encourage contiguous, dense development will increase agricultural productivity. In contrast, for cities with highly fragmented urban development patterns, such as many of those located in Eastern and Southern Europe, anti-sprawl policies, for the benefits of farming, should concentrate on density management. In those cities, further fragmentation could potentially increase agricultural productivity, particularly when the population density is also high.25 These results offer a renewed look at anti-sprawl policies, which are often justified for internalizing environmental impacts, traffic congestion and public services costs associated with urban development (Brueckner, 2001). In this article, we find that anti-sprawl policies can affect farm income by influencing population densities and development patterns. Although some studies have examined the effect of land use and urban growth control policies on total developed areas and population densities (see, e.g. Geshkov and DeSalvo, 2012), relatively few studies have examined their effects on fragmentation. Zoning may well be effective in controlling development inside the protected area, but may generate leapfrog development in the vicinity of the protected area (Irwin and Bockstael, 2004; Wu, 2006). This suggests that it may be difficult to control fragmentation. Fortunately, fragmentation does not significantly affect agricultural productivity when population density is low. When population densities are high and urban development is highly fragmented, further fragmentation will likely enhance agricultural productivity. This suggests that land-use policy for protecting farmland and farm income should be set primarily on the basis of their effectiveness for controlling the density of development, rather than patterns of development. 8. Conclusion This article constitutes a first attempt to assess the effects of two dimensions of urbanization, increasing population density and increasing urban fragmentation, on agricultural productivity in EU countries. We found that while increasing population density will increase agricultural productivity for most European cities, increasing urban fragmentation can have a positive or negative effect on agricultural productivity, depending on the population density and the existing level of urban fragmentation. Although most European cities are still below the threshold of population density, above which further increases in population density will lead to lower agricultural productivity, almost half of the European cities in our sample have already passed the fragmentation threshold, above which further increases in fragmentation will lead to higher agricultural productivity. Agricultural productivity is more sensitive to population density than to urban fragmentation, at least at low and medium density levels. Agricultural productivity becomes more sensitive to urban fragmentation as population density increases. These results are highly robust to alternative strategies to cope with model uncertainty and endogeneity of urban equilibrium covariates. Our results suggest that urban planning policies influencing population density and urban fragmentation can affect agricultural productivity and farm income. Specifically, policies that encourage compact development in a city may increase agricultural productivity and per-hectare farm net returns in the surrounding agricultural areas. In highly fragmented, low-density areas, land use policy should focus on increasing population density. This will not only reduce the negative externalities associated with urban sprawl, but will also increase agricultural productivity. However, literature on this subject is sparse, and further research is needed to fill the gap in the literature and to inform the design of policies targeted for urban growth management and rural development. Supplementary material Supplementary data for this paper are available at Journal of Economic Geography online. Acknowledgements The authors would like to thank Kristian Behrens and two anonymous reviewers for their insightful comments. Funding Walid Oueslati and Julien Salanié acknowledge funding from the European Union by the European Commission within the Seventh Framework Programme in the frame of RURAGRI ERA-NET under Grant Agreement no. 235175 TRUSTEE (ANR-13-RURA-0001-01). The authors only are responsible for any omissions or deficiencies. Neither the TRUSTEE project and any of its partner organizations, nor any organization of the European Union or European Commission are accountable for the content of this research. Footnotes 1 Please see Paül and McKenzie (2013), Pölling et al. (2016), or Wästfelt and Zhang (2016) for recent case studies on the structure and evolution of peri-urban farming in Europe. 2 The Urban Audit database arises from a project coordinated by Eurostat that aims to provide a wide range of indicators of socioeconomic and environmental issues. These indicators are measured across four periods: 1989–1993, 1994–1998, 1999–2002 and 2003–2006. For further details, refer to: http://epp.eurostat.ec.europa.eu/portal/page/portal/region_cities/city_urban. 3 ESPON is a European research program, which provides pan-European evidence and knowledge about European territorial structures, trends, perspectives and policy impacts that enable comparisons among regions and cities. For further details, see: http://database.espon.eu/. 4 These correlations are shown on our sample in Figure A1 of the Online Appendix. 5 Total population represents all residents who have their residence within the LUZ. 6 The Online Appendix lists the 208 cities included in our study and their geographical groupings. 7 We refer the reader to Tosics et al. (2010) for an in-depth description of these classes. 8 To build this instrument, we used the cities listed in the comprehensive survey on strategic bombings from Wikipedia (http://en.wikipedia.org/wiki/Strategic_bombing_during_World_War_II). 9 They do not cover Baltic countries. 10 TL3 Regions per country: Austria (35), Czech Republic (14), Estonia (5), Finland (19), France (94), Greece (13), Hungary (20), Ireland (8), Latvia (6), Poland (66), Slovakia (8), Slovenia (1), Sweden (21). 11 Measured, as in the preceding section, by the number of urban fragments over the total urbanized area. 12 Data, R scripts and results presented in this section and in the appendices are available in the Online Appendix. 13 We also tested the inclusion of an interaction term between FRAG and DENSITY. The effect is not consistently significant. In economic terms, it does not change our core results when significant. This interaction term would also be difficult to instrument so we preferred to present specifications without an interaction term. Table A3 in the Online Appendix reproduces Table 2 with an interaction term. The figure below Table A3 reproduces Figure 2 for a specification [A3.3] where the interaction term is significant. 14 Covariates selection is also consistent with that of bootstrapped stepwise selection (Austin and Tu, 2004) performed both ways using 1000 bootstrapped samples on the same set of candidate covariates. The model selected by bootstrapped stepwise corresponds to the best model identified by BMA. 15 We instrument squared terms to avoid the ‘forbidden regression’ pitfall well described in Angrist and Pischke (2008, 190–192) and Wooldridge (2010, 126–129 and 266–268). 16 While climate covariates determine urban land demand, soil quality and terrain features play on construction costs and aggregate urban land supply. 17 We have also tested specification with a proxy for the crop mix. Crop mix adjustments are one mechanism, through which urbanization affects agricultural productivity. Our core results hold with this additional control (Appendix 2 and Table A6 in the Online Appendix). 18 All first stage regressions are available in the Online Appendix. 19 Based on soil qualification maps. 20 Measured as the standard deviation of terrain elevation in a 10 km radius circle around each settlement. 21 The Bayesian Sargan tests correctly fail to reject our over-identifying exclusion restrictions. As suggested by Kass and Raftery (1995), there is evidence in favor of a theory when the posterior inclusion probability of the corresponding parameter is above 50%. Support is stronger for greater posterior inclusion probabilities. However, West et al. (2003) suggest that parameters with posterior inclusion probabilities above 30% are policy relevant. 22 In Table A5 of the Online Appendix, we give the variance decomposition of density, fragmentation, and the dependent variables. 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( 2011) Urbanization and the viability of local agricultural economies. Land Economics , 87: 109– 125. Google Scholar CrossRef Search ADS   © The Author(s) (2018). Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/about_us/legal/notices) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Economic Geography Oxford University Press

Urbanization and agricultural productivity: some lessons from European cities

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Abstract

Abstract This article evaluates the effect of increasing urbanization on agricultural productivity at the rural-urban fringe for a set of European metropolises. It takes into account changes in total developed area, population density and the level of urban fragmentation associated with urbanization. To cope with endogeneity issues related to urban equilibrium covariates, we set up an instrumental variables strategy based on historical and institutional instruments. Our results indicate that increasing population density increases agricultural productivity at the rural-urban fringe, while increasing urban fragmentation may have a detrimental effect on agricultural productivity at low levels of fragmentation. We use instrumental variable Bayesian model averaging (IVBMA) to address model uncertainty and use an alternative panel dataset to confirm our instrumental strategy. Our results are robust to alternative model specifications and estimation methods. 1. Introduction Although agriculture remains the main user of rural land in many European countries, the amount of farmland has declined, on average, by 4% among the European countries over the last two decades, and this decline is projected to continue (European Environmental Agency, 2006). Most of the farmland loss occurs at the urban fringe on high-quality farmland. Many blame low-density and noncontiguous development, commonly known as urban sprawl, as a primary cause of farmland loss. There are at least three major concerns over the continuing urban sprawl and farmland loss. First, the conversion of the most fertile farmland to development reduces agricultural productivity, which decreases food supply in the short run and threatens food security in the long run. Second, urban sprawl reduces amenities and quality of life in both urban and rural communities. In many places, urban sprawl has encroached into communities to such an extent that the communities themselves have been lost (Wu et al., 2011). Third, urban sprawl may have a detrimental effect on agricultural infrastructure at the urban fringe. With farmland loss, the local agricultural support sector, such as input suppliers or output processors, may lose their businesses because of insufficient demand for their output or insufficient supply of input for their production (Lynch and Carpenter, 2003; Wu et al., 2011). Consequently, agricultural economies may shrink in the short run and become unviable in the long run. Alongside these concerns, urbanization also presents opportunities for agricultural producers at the rural-urban fringe. The emergence of a new customer base provides opportunities for higher value crops. The rapid increase in the number of nurseries, vegetable farms, vineyards, and other high-value crops in many suburban areas show that farmers have remarkable adaptability and capacity to adjust their enterprises to take advantage of the proximity to urban centers.1Lockeretz (1986) examines the characteristics of US counties by their distance to metro areas and finds that counties closer to metro areas tend to have smaller farm sizes, higher intensity, a larger proportion of harvested cropland and a higher standard of living. Larson et al. (2001) report that more than half the value of total US farm production was derived from counties facing urbanization pressure. Lopez et al. (1988) find that when capital gains on land are included, the overall impact of urbanization on profits is positive, although some subsectors of agriculture are adversely affected. The role of agriculture and urbanization has always been at the heart of the debate on sustainable land-use patterns in a modern economy. In this article, we conduct an empirical analysis to evaluate the effect of increasing urbanization on agricultural productivity using data from 282 large urban zones in Europe. We add new insights to the existing literature by analyzing the effect of several dimensions of urbanization on agricultural productivity. These dimensions include changes in total developed area, population density and the level of urban land fragmentation. Our empirical results show that these dimensions affect agricultural productivity in a nonlinear fashion and should be accounted for in urban planning policies. We find that increasing population density increases agricultural productivity while increasing land fragmentation may have a detrimental effect on agricultural productivity at low levels of fragmentation but a positive effect at high levels of fragmentation. Although some studies have examined the effect of urbanization on agriculture in the USA, relatively little research has focused on this issue in Europe, particularly the effect of different dimensions of urbanization on agricultural economies. The next section presents the empirical model and estimation challenges. This is followed by a discussion of data and methodological issues related to the measurement of urbanization in Section 3. Section 4 discusses the estimation strategies, while Section 5 presents the empirical results. Section 6 highlights some policy implications. Section 7 concludes. 2. Empirical model Regional and urban economics literatures reveal that the area, density and patterns of urban development can all affect agricultural productivity at the rural-urban fringe. As a city expands with population growth, a larger customer base will provide opportunities to grow higher-value crops and to market them in new ways (Lockeretz, 1989; Larson et al., 2001). For example, fresh fruits and vegetables can be sold through restaurants and grocery outlets or directly to consumers in farmers markets. In addition, to adapt to rising land values and increasing contact with new residents, farmers may have to change their operations to emphasize higher-value products, more intensive production and enterprises that fit better in an urbanizing environment (Heimlich and Anderson, 2001). Urbanization can also affect agricultural productivity by affecting its critical infrastructure (Lynch and Carpenter, 2003; Wu et al., 2011). For example, with urban development, total cropland will decrease at the rural-urban fringe. This will reduce the demand for agricultural inputs such as fertilizer and seeds. As the demand decreases below a certain threshold, the nearest input supplier may close its business, and the farmer would have to pay more or travel a longer distance for input. Likewise, as the total farmland acreage decreases below a certain threshold, the nearest processor may close, and farmers may have to accept lower output prices or pay additional transport costs for their output. This suggests that even if individual farmers may operate at a constant return to scale, there may be economies of scale at the industry level. Urban development patterns can also affect agricultural productivity. A fragmented development pattern with farms and subdivisions intertwined increases the risk of land use conflicts. Suburban neighbors’ complaints about farm odors, noise and chemical spraying may lead to more stringent land use regulation, which may force farmers to turn to less profitable enterprises (Reynnells, 1987; Van Driesche et al., 1987). Urban smog, theft and vandalism may damage crops. Markets for traditional dairy products or field crops may be reduced as milk-collection routes are curtailed and grain elevators go out of business (Heimlich and Anderson, 2001). To evaluate the effect of area, density and patterns of urban development on agricultural productivity, we estimate the following empirical model using data for a sample of European cities:   πi=f(Ai,Di,Si,Xi;βi)+εi (1) where i is an index of cities, πi is the level of agricultural productivity in city i, Ai is the total developed area, Di is the population density, Si is the degree of urban land fragmentation, Xi is a vector of other covariates affecting agricultural productivity, βi is a vector of parameters and εi is a random error term. When estimating (1), it is important to note that total developed area, population density and urban fragmentation ( Ai, Di,Si) are likely to be endogenous. Standard urban economic theory posits that urbanization increases the demand for urban development, which bids up agricultural land prices. Land conversion expectations and development irreversibility generate a growth premium and an option value, which make up a large portion of farmland values at the rural-urban fringe (Capozza and Helsley, 1990; Plantinga et al., 2002; Cavailhès and Wavresky, 2003; Livanis et al., 2006; Wu and Lin, 2010). In equilibrium, the amounts of land in urban and agricultural uses are determined by equating the rent in urban use to the agricultural rent foregone plus conversion costs and options values (Capozza and Li, 1994; Wu and Chen, 2016). Agricultural land prices capitalize agricultural net returns, growth premium and options values. Changes in agricultural productivity affect land prices and the opportunity cost of land use, which in turn affects the area and pattern of urban development. Thus, efficient estimation of (1) must treat Ai, Di, and Si as potentially endogenous variables. Another major challenge for estimating (1) is model uncertainty. In a closely related paper, Wu et al. (2011) show that in the US net farm income per farmland acre first decreases and then increases with Ai. This suggests that the relationship between farm returns and urbanization may well exhibit nonlinearities. In addition, most of the covariates introduced by Wu et al. (2011) to explain farm returns (e.g. wages in other sectors, median household income, population’s education) were statistically insignificant, although they are theoretically relevant. We thus face uncertainty about the specification of the model. Before presenting the methods used to address these econometric challenges, we first discuss the data used to estimate Equation (1). 3. Data Our data sample was obtained by combining various existing data sources. Our starting point was the complete set of 320 cities included in the Urban Audit (UA) database.2 All cities in the database are defined at three scales: The Core City, which encompasses the administrative boundaries of the city; the Large Urban Zone (LUZ), which is an approximation of the functional urban region centered around the Core city; and the Sub-City District, which is a subdivision of the LUZ (EUROSTAT, 2004). We concentrate on LUZs because farmland development is observed around the fringes of cities. Therefore, the boundaries of each LUZ define the spatial units for this study. UA provides rather limited information on land use, with poor coverage for many cities. As an alternative, we use data on Urban Metropolitan Areas (UMZ), compiled by the European Environment Agency (EEA). Derived from Corine Land Cover, UMZ covers the whole EU-27 at a 200 m resolution for those urban areas that are considered contributing to urban tissue and function (Guerois et al., 2012). Geospatial data on agricultural and nonagricultural areas for each city in 2006 is obtained by superimposing the LUZ boundaries on the UMZ spatial data, using a Geographical Information System (GIS). To illustrate the nature of the spatial data, Figure 1 provides maps documenting the urban (artificial) area for four selected cities: Kielce and Radom (Poland), Eindhoven (Netherlands), and Murcia (Spain). For these cities the figure shows their external boundary and the fragments of urban land. Figure 1 View largeDownload slide Illustration of the urban fragments counting. Figure 1 View largeDownload slide Illustration of the urban fragments counting. The UA data are also supplemented by data obtained from the European Observation Network, Territorial Development and Cohesion (ESPON).3 When combined, these data sources provide a set of explanatory variables covering a broad sample of European cities. Direct measures of agricultural productivity are unavailable for our large sample of European cities. We use agricultural value added per unit of agricultural land (AGRIPROX) to approximate agricultural productivity. This proxy provides a good indicator of farming performance in each city. Data on agricultural value added were obtained from ESPON, and the relevant data on agricultural land area for each LUZ were calculated from the UMZ spatial data. We construct variables to measure the amount of urban development, the level of fragmentation and population density. The total artificial area in square kilometers (ARTIFAREA) is considered as a proxy for all urbanized land in each LUZ. These areas were obtained directly from the spatial UMZ data according to Corine Land Cover nomenclature. This simple measure reflects urban land use in a given area without any prejudgment on internal composition or urban morphology (i.e. the scattered nature of the urban area). Fragmentation measures quantify the degree of discontinuity in development. Scattered development leaves nonused spaces in the built-up areas. In its most simple form, fragmentation is measured as the number of urban patches over the total artificial area (Irwin and Bockstael, 2004; Oueslati et al., 2015) or over population (Arribas-bel et al., 2011). Other measures include the mean patch size (Irwin and Bockstael, 2004; Solon 2009) and the degree of openness, measured by the amount of undeveloped land in the area around an average built-up cell (Burchfield et al., 2006). These are relatively similar ways of describing how fragmented or continuous an urban area is. We construct an index, known as patch density, to reflect urban morphology, in particular, the degree of fragmentation of urban area. The index, which is referred to as the fragmentation index and denoted by FRAG, is calculated by FRAG = FRAGMENTS/ARTIFAREA, where FRAGMENTS represents the number of urban fragments (i.e. individual urban patches) within a specific LUZ. We divide FRAGMENTS by the artificial area within each LUZ to correct for the size effect, since we expect that larger urbanized areas will have more fragments. Figure 1 illustrates the calculation of FRAGMENTS for four cities in the sample. We choose to use only this measure of fragmentation because it is a classical measure of fragmentation (Schneider and Woodcock, 2008; Parent et al., 2009) and because it is highly correlated with other shape metrics such as cohesion, division, edge density and aggregation.4 Moreover, patch density is more coherent with our instrumental strategy. Substituting patch density for other measures of urban fragmentation does not change the results presented here. Population density (DENSITY) is calculated by dividing total population by the total artificial area. Total population for each city is obtained from the ESPON database. The ESPON database also provides comprehensive data for each LUZ on Gross Domestic Product (GDP) adjusted for Purchasing Power Standards and total population (POP).5 We use GDP per capita (GDP_CAP) as a proxy for income that influences consumers’ demand for high-value crops. Higher urban income is expected to increase the demand for high-value crops such as flowers, fruits and vegetable, and thus agricultural value added per hectare. To cope with potential endogeneity issues, in all the following we use lagged GDP per capita (in 2000) and treat GDP_CAP as an exogenous covariate. Furthermore, we added a set of climatic and geographic variables to control for farming potential. The climatic variables include the number of rainy days per year (RAIN), the average temperature of the warmest month in a year (TEMPERATURE) and the average sunshine time per day (SUNSHINE). These variables describe the general climate in the LUZ. A terrain variable, median city center altitude above sea level (MEDALT) is included. This variable is a partial indicator of the ruggedness of the LUZ’s terrain which may have an impact on the potential for farming and urban growth. We also include YWHEAT, the average cereal yield in the area, in the base model. Bosker et al. (2013) provide data on slopes and soil quality for most cities in our sample. We use these data as substitute for our MEDALT and YWHEAT variables in several models. This allows us to check for measurement errors in these variables and, eventually, the endogeneity of YWHEAT. We use highway density (HIGHWAY) from the Eurostat regional data set as a proxy for transport costs. Finally, we include a set of amenity variables to control for the effect of urban development features (in addition to density and patterns) on agricultural productivity. The annual average concentration of NO2 (NO2) is used as an indicator of air pollution in the cities. The number of cinema seats (CINEMA) is used as a proxy for the cultural attractiveness of the central city. A vibrant central city with high environmental and social amenities would be expected to discourage decentralization, and thus may affect the demographic characteristics of urban population and their preferences and demand for agricultural products produced locally. The recorded crime (CRIME) from the Urban Audit is used to account for the security situation in the central city. Patacchini and Zenou (2009) show that European cities with more crime sprawl more. It may also be related to flight from blight phenomena where richer families would move to the city outskirts. These families may exert some social pressure on farmers hence increasing their costs. Darly and Torre (2013) give evidence for the Greater Paris region that these conflicts are important, especially in areas where residents convey an important value to farmland amenities. We gathered partial data on 282 European cities. Considering the availability of agricultural value added and the coverage of Corine Land Cover for 2006, we are left with 208 observations.6 Yet, we do not have information on all potential covariates for each city. The list of potential covariates under study, their definition and the number of cities for which they are available are presented in Table 1. Missing data in our sample have nothing to do with either agricultural value added or urbanization, but relate to the ESPON methodology and countries that did not report the data for given cities. We can treat them as missing completely at random and present unbiased estimates. Table 1 Description of variables Variable  Units  Description  Cases  Mean  Std. Dev.  AGRIPROX  €/ha  Agricultural value added per hectare (purchase power parity)  208  6098  11002  W  Dummy  =1 if western European city, 0 otherwise (North taken as the reference)  208  0.38  0.49  S  Dummy  =1 if southern European city, 0 otherwise (North taken as the reference)  208  0.26  0.44  E  Dummy  =1 if eastern European city, 0 otherwise (North taken as the reference)  208  0.30  0.46  SAREA  1000 km2  Surface area of the city  208  2.08  2.09  SAREA_2  —  SAREA squared  208  8.69  25.71  ARTIFAREA  1000 km2  Artificialized surface area of the city  205  0.29  0.36  ARTIFAREA_2  —  ARTIFAREA squared  205  0.21  0.84  POP  10 millions  Total city Population  208  0.10  0.12  POP_2  —  POP squared  208  0.02  0.10  DENSITY  1000 inh/km2  Inhabitants per km2 of ARTIFAREA  205  5.26  3.97  DENSITY_2  —  DENSITY squared  205  43.30  69.79  FRAG  #/km2  Number of fragments per km2 of ARTIFAREA  205  0.40  0.22  FRAG_2  —  FRAG squared  205  0.20  0.22  GDP_CAP  1000 €/capita  GDP per capita in 2000 (purchase power parity)  208  18.55  8.85  GDP_CAP_2  —  GDP_CAP squared  208  421.99  361.74  YWHEAT  kg/ha  100 kg per hectare  208  48.39  18.56  RAIN  #  Number of rainy days in the year  208  150.71  48.92  SUNSHINE  hrs  Average sunshine time per day  176  5.29  1.25  TEMPERATURE  °C  Average temperature of the warmest months in a year  208  21.71  4.06  NO2  µg/m3  Annual average concentration of NO2  166  28.11  10.73  HIGHWAY  km/km2  Length per surface area  208  29.57  30.89  CRIME  #/inh.  Number per 1000 inhabitants  181  83.59  45.59  BURGLARY  #/inh.  Number per 1000 inhabitants  183  2.91  2.52  ACCESSAIR  Index  Normalized to 100 on the EU mean  177  98.28  36.08  ACCESSRAIL  Index  Normalized to 100 on the EU mean  172  94.12  65.47  ACCESSROAD  Index  Normalized to 100 on the EU mean  173  92.77  58.13  CINEMA  #/inh.  Number of cinema seats per 1000 inhabitants  193  17.16  9.52  GREENSPACE  ha  Surface area in hectare  156  41.38  56.94  MEDALT  100 meters  Median city center altitude above sea level  208  1.31  1.39  MEDALT_2  —  MEDALT squared  208  3.64  7.84  Variable  Units  Description  Cases  Mean  Std. Dev.  AGRIPROX  €/ha  Agricultural value added per hectare (purchase power parity)  208  6098  11002  W  Dummy  =1 if western European city, 0 otherwise (North taken as the reference)  208  0.38  0.49  S  Dummy  =1 if southern European city, 0 otherwise (North taken as the reference)  208  0.26  0.44  E  Dummy  =1 if eastern European city, 0 otherwise (North taken as the reference)  208  0.30  0.46  SAREA  1000 km2  Surface area of the city  208  2.08  2.09  SAREA_2  —  SAREA squared  208  8.69  25.71  ARTIFAREA  1000 km2  Artificialized surface area of the city  205  0.29  0.36  ARTIFAREA_2  —  ARTIFAREA squared  205  0.21  0.84  POP  10 millions  Total city Population  208  0.10  0.12  POP_2  —  POP squared  208  0.02  0.10  DENSITY  1000 inh/km2  Inhabitants per km2 of ARTIFAREA  205  5.26  3.97  DENSITY_2  —  DENSITY squared  205  43.30  69.79  FRAG  #/km2  Number of fragments per km2 of ARTIFAREA  205  0.40  0.22  FRAG_2  —  FRAG squared  205  0.20  0.22  GDP_CAP  1000 €/capita  GDP per capita in 2000 (purchase power parity)  208  18.55  8.85  GDP_CAP_2  —  GDP_CAP squared  208  421.99  361.74  YWHEAT  kg/ha  100 kg per hectare  208  48.39  18.56  RAIN  #  Number of rainy days in the year  208  150.71  48.92  SUNSHINE  hrs  Average sunshine time per day  176  5.29  1.25  TEMPERATURE  °C  Average temperature of the warmest months in a year  208  21.71  4.06  NO2  µg/m3  Annual average concentration of NO2  166  28.11  10.73  HIGHWAY  km/km2  Length per surface area  208  29.57  30.89  CRIME  #/inh.  Number per 1000 inhabitants  181  83.59  45.59  BURGLARY  #/inh.  Number per 1000 inhabitants  183  2.91  2.52  ACCESSAIR  Index  Normalized to 100 on the EU mean  177  98.28  36.08  ACCESSRAIL  Index  Normalized to 100 on the EU mean  172  94.12  65.47  ACCESSROAD  Index  Normalized to 100 on the EU mean  173  92.77  58.13  CINEMA  #/inh.  Number of cinema seats per 1000 inhabitants  193  17.16  9.52  GREENSPACE  ha  Surface area in hectare  156  41.38  56.94  MEDALT  100 meters  Median city center altitude above sea level  208  1.31  1.39  MEDALT_2  —  MEDALT squared  208  3.64  7.84  Table 1 Description of variables Variable  Units  Description  Cases  Mean  Std. Dev.  AGRIPROX  €/ha  Agricultural value added per hectare (purchase power parity)  208  6098  11002  W  Dummy  =1 if western European city, 0 otherwise (North taken as the reference)  208  0.38  0.49  S  Dummy  =1 if southern European city, 0 otherwise (North taken as the reference)  208  0.26  0.44  E  Dummy  =1 if eastern European city, 0 otherwise (North taken as the reference)  208  0.30  0.46  SAREA  1000 km2  Surface area of the city  208  2.08  2.09  SAREA_2  —  SAREA squared  208  8.69  25.71  ARTIFAREA  1000 km2  Artificialized surface area of the city  205  0.29  0.36  ARTIFAREA_2  —  ARTIFAREA squared  205  0.21  0.84  POP  10 millions  Total city Population  208  0.10  0.12  POP_2  —  POP squared  208  0.02  0.10  DENSITY  1000 inh/km2  Inhabitants per km2 of ARTIFAREA  205  5.26  3.97  DENSITY_2  —  DENSITY squared  205  43.30  69.79  FRAG  #/km2  Number of fragments per km2 of ARTIFAREA  205  0.40  0.22  FRAG_2  —  FRAG squared  205  0.20  0.22  GDP_CAP  1000 €/capita  GDP per capita in 2000 (purchase power parity)  208  18.55  8.85  GDP_CAP_2  —  GDP_CAP squared  208  421.99  361.74  YWHEAT  kg/ha  100 kg per hectare  208  48.39  18.56  RAIN  #  Number of rainy days in the year  208  150.71  48.92  SUNSHINE  hrs  Average sunshine time per day  176  5.29  1.25  TEMPERATURE  °C  Average temperature of the warmest months in a year  208  21.71  4.06  NO2  µg/m3  Annual average concentration of NO2  166  28.11  10.73  HIGHWAY  km/km2  Length per surface area  208  29.57  30.89  CRIME  #/inh.  Number per 1000 inhabitants  181  83.59  45.59  BURGLARY  #/inh.  Number per 1000 inhabitants  183  2.91  2.52  ACCESSAIR  Index  Normalized to 100 on the EU mean  177  98.28  36.08  ACCESSRAIL  Index  Normalized to 100 on the EU mean  172  94.12  65.47  ACCESSROAD  Index  Normalized to 100 on the EU mean  173  92.77  58.13  CINEMA  #/inh.  Number of cinema seats per 1000 inhabitants  193  17.16  9.52  GREENSPACE  ha  Surface area in hectare  156  41.38  56.94  MEDALT  100 meters  Median city center altitude above sea level  208  1.31  1.39  MEDALT_2  —  MEDALT squared  208  3.64  7.84  Variable  Units  Description  Cases  Mean  Std. Dev.  AGRIPROX  €/ha  Agricultural value added per hectare (purchase power parity)  208  6098  11002  W  Dummy  =1 if western European city, 0 otherwise (North taken as the reference)  208  0.38  0.49  S  Dummy  =1 if southern European city, 0 otherwise (North taken as the reference)  208  0.26  0.44  E  Dummy  =1 if eastern European city, 0 otherwise (North taken as the reference)  208  0.30  0.46  SAREA  1000 km2  Surface area of the city  208  2.08  2.09  SAREA_2  —  SAREA squared  208  8.69  25.71  ARTIFAREA  1000 km2  Artificialized surface area of the city  205  0.29  0.36  ARTIFAREA_2  —  ARTIFAREA squared  205  0.21  0.84  POP  10 millions  Total city Population  208  0.10  0.12  POP_2  —  POP squared  208  0.02  0.10  DENSITY  1000 inh/km2  Inhabitants per km2 of ARTIFAREA  205  5.26  3.97  DENSITY_2  —  DENSITY squared  205  43.30  69.79  FRAG  #/km2  Number of fragments per km2 of ARTIFAREA  205  0.40  0.22  FRAG_2  —  FRAG squared  205  0.20  0.22  GDP_CAP  1000 €/capita  GDP per capita in 2000 (purchase power parity)  208  18.55  8.85  GDP_CAP_2  —  GDP_CAP squared  208  421.99  361.74  YWHEAT  kg/ha  100 kg per hectare  208  48.39  18.56  RAIN  #  Number of rainy days in the year  208  150.71  48.92  SUNSHINE  hrs  Average sunshine time per day  176  5.29  1.25  TEMPERATURE  °C  Average temperature of the warmest months in a year  208  21.71  4.06  NO2  µg/m3  Annual average concentration of NO2  166  28.11  10.73  HIGHWAY  km/km2  Length per surface area  208  29.57  30.89  CRIME  #/inh.  Number per 1000 inhabitants  181  83.59  45.59  BURGLARY  #/inh.  Number per 1000 inhabitants  183  2.91  2.52  ACCESSAIR  Index  Normalized to 100 on the EU mean  177  98.28  36.08  ACCESSRAIL  Index  Normalized to 100 on the EU mean  172  94.12  65.47  ACCESSROAD  Index  Normalized to 100 on the EU mean  173  92.77  58.13  CINEMA  #/inh.  Number of cinema seats per 1000 inhabitants  193  17.16  9.52  GREENSPACE  ha  Surface area in hectare  156  41.38  56.94  MEDALT  100 meters  Median city center altitude above sea level  208  1.31  1.39  MEDALT_2  —  MEDALT squared  208  3.64  7.84  4. Empirical strategy When estimating (1), we control for major confounding factors affecting agricultural productivity, including soil quality, slope, climate and urban features such as average income and amenities. However, there may be potential unobservables correlated with both the urban equilibrium covariates (Ai, Di and Si) and agricultural productivity and it is difficult to have a strong prior on the sign of the bias induced by the potential endogeneity of urban covariates. To gain insights on this issue, we pursue an instrumental variable strategy, complemented by a separate panel data analysis. As reported later in the article, both approaches yield similar conclusions. 4.1. Instrumental variables We collect two sets of institutional and historical instruments thought to be correlated with urban covariates but not with agricultural productivity. Spatial planning policies drive urban development, influencing its density and fragmentation. There is a great deal of variety in spatial planning governance among European countries (Tosics et al., 2010). We build a set of institutional instruments at the country level describing the coordination among the multilevel jurisdictions in charge of spatial planning in different European countries, based on the typology provided by Tosics et al. (2010, Figure 2, p. 40). Their typology encompasses several important dimensions of spatial planning policies such as, inter alia, the prerogatives of different jurisdictional levels (local, regional and national levels), the locus of power (decentralized or centralized), the relative roles of the public and private sectors, the maturity of the spatial planning system and the discrepancies between goals and achievements of those policies. Their typology yields four classes of spatial planning approaches: the ‘regional economic planning approach’ pursuing a large set of goals driven by the central government like in France, the ‘comprehensive integrated approach’ relying on the coordination of national and regional plans such as in Germany, the ‘land use management’ approach with a large role played by local jurisdictions as it is in the UK, and the ‘urbanism’ tradition, encountered in several Mediterranean countries, focusing on the city and its architecture via townscape and building controls.7 Additionally, we build two other variables describing land-use policies from Silva and Acheampong (2014) who survey land-use planning policies in OECD countries. First, we build a dummy for countries in which competences are mainly at the subnational level, versus national or shared between these two levels (Silva and Acheampong, 2014, Table 2, p. 14). We also build a variable describing the level of coordination in planning following two dimensions: verticality (coordination between national and subnational jurisdictions) and horizontality (coordination among sectoral policies). Silva and Acheampong (2014, Table 6, p. 36) identifies four classes of OECD countries where land-use planning is mainly vertical, mainly horizontal, strongly integrated in both dimensions or weakly coordinated in both dimensions. We believe that we can safely put an exclusion restriction on these institutional instruments because they are derived from historical determinants uncorrelated with agricultural productivity. Table 2 Ordinary least squares estimates   [1]  [2]  [3]  [4]  [5]  [6]  SAREA  −0.212***  −0.347***  −0.316***  −0.148**  −0.270***  −0.226***  (0.065)  (0.082)  (0.087)  (0.066)  (0.077)  (0.079)  SAREA_2    0.017***  0.016***    0.012***  0.010***    (0.005)  (0.005)    (0.004)  (0.004)  POP  0.879  −0.713  −1.235  0.882  1.516  0.954  (0.710)  (1.180)  (1.250)  (0.808)  (1.434)  (1.469)  POP_2    0.464  0.772    −1.361  −1.071    (0.786)  (0.798)    (0.990)  (1.008)  DENSITY  0.147***  0.375***    0.232***  0.424***    (0.025)  (0.065)    (0.032)  (0.057)    DENSITY_2    −0.012***      −0.013***      (0.003)      (0.003)    log(DENSITY)      1.051***      1.275***      (0.167)      (0.118)  FRAG  −1.149***  −5.297***  −5.632***  −0.973**  −5.327***  −5.708***  (0.329)  (0.953)  (0.952)  (0.436)  (1.217)  (1.180)  FRAG_2    4.681***  4.845***    5.007***  5.181***    (0.903)  (0.891)    (1.153)  (1.108)  Additional covariates  A  A + B  A + B  A + C  A + B + C  A + B + C  Adjusted-R2  0.539  0.681  0.686  0.630  0.748  0.760  Observations  173  173  173  108  108  108    [1]  [2]  [3]  [4]  [5]  [6]  SAREA  −0.212***  −0.347***  −0.316***  −0.148**  −0.270***  −0.226***  (0.065)  (0.082)  (0.087)  (0.066)  (0.077)  (0.079)  SAREA_2    0.017***  0.016***    0.012***  0.010***    (0.005)  (0.005)    (0.004)  (0.004)  POP  0.879  −0.713  −1.235  0.882  1.516  0.954  (0.710)  (1.180)  (1.250)  (0.808)  (1.434)  (1.469)  POP_2    0.464  0.772    −1.361  −1.071    (0.786)  (0.798)    (0.990)  (1.008)  DENSITY  0.147***  0.375***    0.232***  0.424***    (0.025)  (0.065)    (0.032)  (0.057)    DENSITY_2    −0.012***      −0.013***      (0.003)      (0.003)    log(DENSITY)      1.051***      1.275***      (0.167)      (0.118)  FRAG  −1.149***  −5.297***  −5.632***  −0.973**  −5.327***  −5.708***  (0.329)  (0.953)  (0.952)  (0.436)  (1.217)  (1.180)  FRAG_2    4.681***  4.845***    5.007***  5.181***    (0.903)  (0.891)    (1.153)  (1.108)  Additional covariates  A  A + B  A + B  A + C  A + B + C  A + B + C  Adjusted-R2  0.539  0.681  0.686  0.630  0.748  0.760  Observations  173  173  173  108  108  108  Note: Dependent variable: log(AGRIPROX). Robust standard-errors in parentheses. ***, **, *: significance at the 1%, 5% and 10% levels, respectively. A: a constant, regional dummies (W, S and E), income per inhabitant (GDP_CAP), agricultural productivity determinants (YWHEAT, RAIN, SUNSHINE, TEMPERATURE, MEDALT). B: squared terms on continuous covariates (GDP_CAP, YWHEAT, RAIN, SUNSHINE, TEMPERATURE, MEDALT). C: city amenities (CRIME, BURGLARY, ACCESSRAIL, ACCESSROAD, CINESEATS and GREENSPACE). Table 2 Ordinary least squares estimates   [1]  [2]  [3]  [4]  [5]  [6]  SAREA  −0.212***  −0.347***  −0.316***  −0.148**  −0.270***  −0.226***  (0.065)  (0.082)  (0.087)  (0.066)  (0.077)  (0.079)  SAREA_2    0.017***  0.016***    0.012***  0.010***    (0.005)  (0.005)    (0.004)  (0.004)  POP  0.879  −0.713  −1.235  0.882  1.516  0.954  (0.710)  (1.180)  (1.250)  (0.808)  (1.434)  (1.469)  POP_2    0.464  0.772    −1.361  −1.071    (0.786)  (0.798)    (0.990)  (1.008)  DENSITY  0.147***  0.375***    0.232***  0.424***    (0.025)  (0.065)    (0.032)  (0.057)    DENSITY_2    −0.012***      −0.013***      (0.003)      (0.003)    log(DENSITY)      1.051***      1.275***      (0.167)      (0.118)  FRAG  −1.149***  −5.297***  −5.632***  −0.973**  −5.327***  −5.708***  (0.329)  (0.953)  (0.952)  (0.436)  (1.217)  (1.180)  FRAG_2    4.681***  4.845***    5.007***  5.181***    (0.903)  (0.891)    (1.153)  (1.108)  Additional covariates  A  A + B  A + B  A + C  A + B + C  A + B + C  Adjusted-R2  0.539  0.681  0.686  0.630  0.748  0.760  Observations  173  173  173  108  108  108    [1]  [2]  [3]  [4]  [5]  [6]  SAREA  −0.212***  −0.347***  −0.316***  −0.148**  −0.270***  −0.226***  (0.065)  (0.082)  (0.087)  (0.066)  (0.077)  (0.079)  SAREA_2    0.017***  0.016***    0.012***  0.010***    (0.005)  (0.005)    (0.004)  (0.004)  POP  0.879  −0.713  −1.235  0.882  1.516  0.954  (0.710)  (1.180)  (1.250)  (0.808)  (1.434)  (1.469)  POP_2    0.464  0.772    −1.361  −1.071    (0.786)  (0.798)    (0.990)  (1.008)  DENSITY  0.147***  0.375***    0.232***  0.424***    (0.025)  (0.065)    (0.032)  (0.057)    DENSITY_2    −0.012***      −0.013***      (0.003)      (0.003)    log(DENSITY)      1.051***      1.275***      (0.167)      (0.118)  FRAG  −1.149***  −5.297***  −5.632***  −0.973**  −5.327***  −5.708***  (0.329)  (0.953)  (0.952)  (0.436)  (1.217)  (1.180)  FRAG_2    4.681***  4.845***    5.007***  5.181***    (0.903)  (0.891)    (1.153)  (1.108)  Additional covariates  A  A + B  A + B  A + C  A + B + C  A + B + C  Adjusted-R2  0.539  0.681  0.686  0.630  0.748  0.760  Observations  173  173  173  108  108  108  Note: Dependent variable: log(AGRIPROX). Robust standard-errors in parentheses. ***, **, *: significance at the 1%, 5% and 10% levels, respectively. A: a constant, regional dummies (W, S and E), income per inhabitant (GDP_CAP), agricultural productivity determinants (YWHEAT, RAIN, SUNSHINE, TEMPERATURE, MEDALT). B: squared terms on continuous covariates (GDP_CAP, YWHEAT, RAIN, SUNSHINE, TEMPERATURE, MEDALT). C: city amenities (CRIME, BURGLARY, ACCESSRAIL, ACCESSROAD, CINESEATS and GREENSPACE). We also define a dummy for former communist countries, where both the tradition of planning and the turn to a market economy may have impacted urban development (Musil, 1993; Sailer-Fliege, 1999). Furthermore, we collect data on cities that were strategically bombed during World War II.8 It has been shown that cities suffering from high destruction may recover fully in a quarter century (Davis and Weinstein, 2002; Miguel and Roland, 2011). They are thus unlikely to be correlated with agricultural productivity. However, most cities suffering from strategic bombing during World War II were heavily destroyed and the building stock had to be rebuilt, following modern urbanism patterns, compared with cities that were not bombed. We thus believe these variables to be correlated with our cities descriptors but not with agricultural productivity and are suitable instruments. Our identification strategy also relies on a set of historical variables, known to be related to city growth. First, we aggregate Acemoglu et al. (2005) data using current cities functional area delimitations (see Section 3). These data describe the population of European cities reaching 5000 inhabitants somewhere between 1400 and 1800. A primary source for these data is Bairoch et al. (1988). From these data, we compute the number of cities that reached 5000 inhabitants before 1800 in each Urban Morphological Zones (UMZ), aggregate population in 1400 and 1800, and population growth between these two dates. In parallel, we use data from Bosker et al. (2013) to build a second set of potential historical instruments. Data from Bosker et al. (2013) also rely on Bairoch et al. (1988), however not covering all European countries under scrutiny in our analysis.9 They span a larger time horizon allowing us to collect data on aggregate population in 1000 and 1400, and population growth between these two dates. Finally, we also use Bosker et al. (2013) to code cities that were on a roman commercial route. It may be argued that the historical development of cities is related to local agricultural potential, in which case using past urbanization as an instrument may be problematic because it would be correlated with contemporary agricultural productivity. Nunn and Quian (2011) show that a higher agricultural potential played a role in the development of European cities before 1900. However, this link is debated (Bosker et al., 2013). In our case, we believe that we can safely put an exclusion restriction on our historical variables for the following reasons. First, and foremost, we control for agricultural potential using nonexcluded instruments related to soil quality, climate and terrain slopes. Second, these links are unlikely to hold in the 21st century. Most of cities’ growth in Europe took place during the 20th century (UN, 2009) and there has been an explosion in agricultural productivity after World War II. Following Bairoch (1997), crops yields have been almost constant in Europe throughout 1800–1950 and multiplied by 3 to 6 between 1950 and 1990. For instance, in France, average wheat yields stayed below 2 tons per hectare (t/ha) between 1815 and 1950, then exploded to more than 4 t/ha in 1980 and more than 8 t/ha in 2001 (Bouchet, 2010). Bairoch (1997) labels this period the ‘third agricultural revolution’. The great improvements in mechanization, animal and plant genetics, mineral pesticides and fertilizers, and the development of the agri-food industry after World War II have profoundly changed and redrawn farming throughout Europe. Hence, soil quality, climate and terrain slopes are likely to be the primary determinants of agricultural productivity that affect urbanization in both the remote past and the present. Our control of these primary determinants ensures the validity of our exclusion restrictions. 4.2. Robustness checks Using deep lags to instrument urban equilibrium strengthens our exclusion restrictions but it may also weaken instrumentation (Stock et al., 2002; Combes et al., 2010; Combes et al., 2011). Moreover, using institutional variables at the national level as instruments can only capture the cross-country variation in urbanization features. For these reasons, the strength of our instruments is uncertain. In the next section we will see that, indeed, while urban equilibrium variables in level (population or artificialized area) are well instrumented, partial F-tests for the instrumentation of density and fragmentation generally lie between 5 and 10. To overcome potential weak instruments issues, we conduct four robustness checks. First, we make use of heteroscedasticity related to nonexcluded instruments in the first stage regressions to build additional internal instruments in the way suggested by Lewbel (2012). This heteroscedasticity is particularly important in the density and fragmentation first-stage regressions and this strategy slightly strengthens our instrumental strategy. Second, we estimate the model using instrumental variables estimators less sensitive to weak instruments (Stock et al., 2002; Chao and Swanson, 2005), including the limited information maximum likelihood estimator (LIML) and the generalized method of continuously-updated moments estimator (GMM-CUE; Hansen et al., 1996). Our results are robust to these alternative estimators. Third, we rely on a Bayesian model averaging (hereafter BMA) framework. Rather than choosing a single model, on a goodness-of-fit or information criterion, to represent the knowledge we have on the process under study, BMA proposes to average over a wide range of models weighted by the strength of empirical evidence in favor of each model called posterior probability in a Bayesian framework. Detailed discussions of BMA can be found in Raftery et al. (1997), Hoeting et al. (1999) and Wasserman (2000). Moral-Benito (2015) offers a review of model averaging applied to economics. This framework allows tackling two issues simultaneously: model uncertainty and a potential weak instrument issue. As underlined earlier, we have strong reasons to believe that the effect of urbanization on agricultural productivity is nonlinear. As widely discussed in the literature, urbanization presents both opportunities and challenges to agriculture. The positive effects may dominate the negative effects at some levels of urbanization, but not at others. Previous empirical analysis of US data indicates that the relationship is nonlinear. For example, Wu et al. (2011) find that in the US net farm income per farmland acre first decreases and then increases with total developed area. The BMA is particularly suited for estimation and inference problems when we are uncertain of which model to choose based on strong empirical evidence or theoretical grounds. Aside from potential nonlinearities, model uncertainty arises because we also include a large set of amenity variables that may indirectly affect agricultural productivity through changes in demographics and labor market conditions as suggested by Glaeser et al. (2001), which may in turn affect demand for agricultural goods and capital and labor costs for farmers. In our setting, we address uncertainty in both stages of our instrumental variable strategy using an extension of the BMA approach to IV models: Instrumental Variable Bayesian Model Averaging (IVBMA). Drawing on earlier work by Kleibergen and Zivot (2003), several authors have recently attempted to develop a methodology to simultaneously address model uncertainty and instrumental variable estimation (Karl and Lenkoski, 2012; Koop et al., 2012; Lenkoski et al., 2014). Lenkoski et al. (2014) developed an IVBMA approach using a two-stage extension of the unit information prior, addressing model uncertainty in both stages. The full approach is extensively described in Lenkoski et al. (2014) and Eicher and Kuenzel (2016). Karl and Lenkoski (2012) developed an IVBMA algorithm which nests an MC3 algorithm within a Gibbs sampler allowing for simultaneous selection on both stages of the model. This approach has been used in recent applications to models of growth (Eicher and Kuenzel, 2016) and models of export diversification (Jetter and Ramírez Hassan, 2015). As stressed by Lenkoski et al. (2014), IVBMA has several interesting features, including limiting over identification issues and indicating the strength of covariates in both stages. We show that our core results are robust to these alternative strategies. Fourth, we further assess the robustness of our results using an alternative panel dataset constructed using OECD Territorial Level 3 (TL3) regions statistics for 2000, 2006 and 2012. TL3 regions are the smallest administrative unit available throughout Europe. They are closely similar to NUTS3 regions in the European classification (Eurostat). TL3 regions are administrative areas and not defined on a functional basis. Nevertheless, in most European countries, these regions have been established around a major city. Hence, we expect our main results to hold at this administrative level though they may be less strong due to the fact that the effects of urban structure on agricultural productivity will be partially hidden, at this geographical scale, by other determinants. We identified 310 TL3 regions covering 13 European countries10 in 2000, 2006 and 2012 for which we have data on gross value added (GVA) and employment in the agricultural sector, population and GDP per capita. Using the panel data, we estimate a fixed-effects panel data model similar to (1) including the covariates and their squared terms. The estimated model is:   Yit=αi+γt+βXit+ɛit, (2) where Yit is our proxy for agricultural productivity, either linear and log-transformed; Xit is a vector of covariates including total population in the TL3 region, population density, our proxy for urban land fragmentation,11 and GDP per capita; αi represents the TL3 regions fixed effect; and γt is the time fixed-effect. The inclusion of TL3 regions fixed-effect controls for time invariant unobservables potentially correlated with urbanization. Estimating (2) by OLS yields an unbiased estimate of β under the strict exogeneity assumption covXit,ɛit=0. Again, we are able to show that our core results hold using this completely different approach. 5. Empirical results12 We first report results from the OLS estimation and then turn to our main results using Instrumental Variable (IV) approaches for different sets of instruments. We then test the robustness of our results showing that they hold under different specifications: adding artificial instruments, using alternative estimators, using Instrumental Bayesian Model Averaging (IVBMA) and using an alternative panel data set to estimate a similar fixed effects model. We show that our main results hold in these different settings. Finally, we discuss the relationship between the features of urban development and agricultural productivity implied by the results. 5.1. Results from OLS estimations Before turning to the IV estimation, we explored simple models relating agricultural value added per hectare (AGRIPROX) to covariates of interest such as DENSITY (Dj), FRAG (Sj), SAREA (Aj) and POP. In all these preliminary models, we searched for Box-Cox transformations of AGRIPROX. All cases pointed unambiguously to the logarithmic transformation. Hence, in the following, we consider only log-linear models where log(AGRIPROX) is the dependent variable. In Table 2, Model [1] includes all covariates of interest (SAREA, POP, DENSITY and FRAG) and controls linearly. The effect of DENSITY is positive while the effects of FRAG and SAREA are negative. Model [2] introduces quadratic terms.13 All are significant but POP and POP_2. The insignificance of POP and POP_2 may be due to the fact that the effect of total population is captured by total surface area (SAREA) and population density (DENSITY). Estimates on DENSITY and DENSITY_2 indicate a concave relationship between agricultural productivity and density. This relationship is strictly increasing over almost the entire observed range of DENSITY in our sample. We thus also estimated models with log(DENSITY), which turns out to be our preferred specification (model [3]). Estimates on FRAG and FRAG_2 imply a convex U-shape relationship between land fragmentation and agricultural productivity in our sample of European cities. Table 2 presents results with alternative control variables. The first set of controls (A) includes regional dummies (W, S and E), average income per inhabitant (GDP_CAP) and agricultural productivity determinants (YWHEAT, RAIN, SUNSHINE, TEMPERATURE, MEDALT). The second set of controls (A + B) includes those in the first set as well as the squared terms of all continuous controls. The third set of control (A + C) includes those in first set and some city amenity measures (CRIME, BURGLARY, ACCESSRAIL, ACCESSROAD, CINESEATS and GREENSPACE), and the fourth set of controls (A + B + C) include those included in the second set and the city amenity measures. Results in Table 2 show that our estimates of parameters of interest are robust to changes in controls, at least qualitatively.14 5.2. Results from the IV approaches We now turn to the instrumental variable estimates, which constitute our main results. We use four sets of instruments to identify the effects of urban equilibrium covariates. We instrument SAREA, POP, FRAG, and their squared terms15 and log(DENSITY). Note, however, that we are controlling for strong exogenous factors determining both agricultural and urban rents16 such as farmland quality (YWHEAT), climate (RAIN, SUNSHINE and TEMPERATURE) and terrain features (MEDALT), thus certainly purging a nonnegligible part of potential endogeneity issues.17 To further explore potential bias in our estimates of the urban covariates at the heart of our argument, we propose several IV approaches, which we believe give much support to the results presented in Table 2. Two-stage least squares (2SLS) IV estimates18 using institutional and historical instruments discussed in Section 4.1 are presented in Table 2. Models [1], [2], [3] and [4] rely on the institutional and historical instruments related to spatial planning described earlier, dummies for former communist countries, and World War II strategic bombings. They also make use of Acemoglu et al. (2005) data on urbanization including the number of cities that reached 5000 inhabitants before 1800, aggregate population in the LUZ in 1400, and population growth in the LUZ between 1400 and 1800, along with their squared terms. These models are over-identified (14 instruments). Reduced form regressions confirm the significance of these institutional and historical instruments and the results are consistent with intuition. For instance, former communist countries’ cities tend to be larger, less dense and more fragmented. Cities in countries with stronger national control on planning policies tend to be larger while cities in countries with a regional economic approach to spatial planning policies tend to be more fragmented. Cities in countries where spatial planning relies on a comprehensive integrated approach are denser. A strong degree of vertical and horizontal coordination in spatial planning policies is related to denser cities. Cities with more developed communities in 1800 or larger population in 1400 tend to be larger and less fragmented today. Cities with a larger increase in population between 1400 and 1800 also tend to be less dense and less fragmented today. Overall, first-stage equations adjusted-R2 and partial F-tests corresponding to the excluded instruments suggest that our instruments are not weak. Sargan tests correctly fail to reject our over-identifying exclusion restrictions. Wu–Hausman tests fail to reject differences between OLS and IV. This is partly due to the fact that OLS bias may be small because we control for climate, slopes and soil quality. 5.3. Robustness checks results We also estimate the model using estimators less sensitive to small sample bias and large numbers of instruments (LIML and GMM-CUE). The results are generally robust to the choice of estimators (e.g. model [3]). Model [4] makes use of different instruments less deeply lagged in the past. Instead of using aggregate population in the LUZ in 1400, we use the same measure for 1800. We also skip population growth in the LUZ between 1400 and 1800 for a built-in estimate of density in 1800 constructed by dividing population in 1800 by the number of cities inside the LUZ. We get very similar results. To strengthen our point, we also make use of heteroscedasticity related to nonexcluded instruments in the first-stage regressions to build additional internal instruments in the way suggested by Lewbel (2012). This heteroscedasticity is particularly important in the density and fragmentation first-stage regressions. 2SLS estimates using additional internal instruments are presented in column [5]. Slightly larger first-stage partial F-tests indicate that it moderately strengthens our IV strategy. Model [6] presents results from the same model using GMM-CUE. Models [7] and [8] present similar estimates using our fourth set of instruments. We substitute Acemoglu et al. (2005) data for that of Bosker et al. (2013). We now use population in 1400, population growth between 1000 and 1400 and their squared terms and a Roman road hub dummy as instruments. In these models, we also substitute YWHEAT for their Bosker et al. soil quality variable19 and MEDALT and MEDALT_2 for their terrain ruggedness measures20 and its square. Our IV strategy confirms the key roles of density and fragmentation in explaining agricultural productivity. There is an increasing and concave relationship between agricultural productivity and urban density and a U-shape relationship with urban fragmentation. These results are robust to different IV strategies, estimators and sample sizes. We conduct additional robustness checks of our main results using an IVBMA model (Karl and Lenkoski, 2012; Lenkoski et al., 2014), which addresses model uncertainty at both stages of the IV estimation. IVBMA estimates are reported in Table A4 of the Online Appendix. The posterior probabilities of inclusion of our parameters of interest are high, indicating that there is little uncertainty about their key role in determining agricultural productivity.21 The posterior estimates have the same sign as in the IV models. Regional dummies and SUNSHINE are also included in almost all models. Again, the IVBMA approaches confirm the key roles of density and fragmentation in explaining agricultural productivity. Results from the panel data model are presented in Table 4. Panel A of the table shows the effect of our covariates of interest on GVA per worker (models [1] and [2]) and its logarithm (models [3] and [4]) using alternatively DENSITY and its squared term and log(DENSITY) as explanatory variables. These results confirm that agricultural productivity is increasing and concave with respect to regional density and the U-shape relationship with regional urban fragmentation. However, the statistical significance of the effect of density is sensitive to model specifications.22 Controlling further for total urbanized area does not change the results. In contrast to the cross-sectional model results, population becomes significant in the panel data model, maybe because the panel data model can better capture the effect of population growth on agricultural productivity. Panel B of Table 4 shows the results of the same models using GVA per hectare as the dependent variable. The results are consistent with those of panel A. Altogether, the robustness checks conducted using the panel data set, built independently from our main cross-section data set, reinforce our conclusions on the links between agricultural productivity and urban density and fragmentation. Table 3 Instrumental variables estimates   [1] IV (2SLS)   [2] IV (2SLS)   [3] IV (GMM-CUE)   [4] IV (2SLS)   Variable  Coef.  Std. Err.  Coef.  Std. Err.  Coef.  Std. Err.  Coef.  Std. Err.  SAREA  −0.304  0.304  −0.295**  0.130  −0.131  0.161  −0.244*  0.142  SAREA_2  0.012  0.012  0.011  0.008  0.002  0.009  0.007  0.008  POP  0.295  3.772              POP_2  −0.455  1.899              log(DENSITY)  1.207**  0.465  1.166***  0.275  1.009***  0.268  1.199***  0.241  FRAG  −9.674**  4.521  −9.680***  3.093  −8.998***  3.334  −9.386***  2.878  FRAG_2  9.365**  4.358  9.342***  3.492  8.511**  3.569  8.983***  3.202  Additional covariates  A  A  A  A  Adjusted-R2  0.622  0.632  —  0.642  Observations  154  154  154  154  Instruments  Institutional & historical (1)  Institutional & historical (1)  Institutional & historical (1)  Institutional & historical (2)    Partial F  Adj.-R2  Partial F  Adj.-R2  —  —  Partial F  Adj.-R2  SAREA  29.12***  0.519  29.12***  0.519  —  —  42.24***  0.584  SAREA_2  58.57***  0.280  58.57***  0.280  —  —  30.52***  0.400  POP  59.37***  0.741      —  —      POP_2  189.17***  0.910      —  —      log(DENSITY)  7.52***  0.664  7.52***  0.664  —  —  7.60***  0.663  FRAG  9.27***  0.403  9.27***  0.403  —  —  9.43***  0.415  FRAG_2  5.40***  0.336  5.40***  0.336  —  —  5.48***  0.341  No. of excluded instruments  14  14  14  12  Wu–Hausman test  1.402  2.042*  —  2.302**  Sargan test  17.442**  17.785**  Hansen J-Test: 10.981*  18.637**    [1] IV (2SLS)   [2] IV (2SLS)   [3] IV (GMM-CUE)   [4] IV (2SLS)   Variable  Coef.  Std. Err.  Coef.  Std. Err.  Coef.  Std. Err.  Coef.  Std. Err.  SAREA  −0.304  0.304  −0.295**  0.130  −0.131  0.161  −0.244*  0.142  SAREA_2  0.012  0.012  0.011  0.008  0.002  0.009  0.007  0.008  POP  0.295  3.772              POP_2  −0.455  1.899              log(DENSITY)  1.207**  0.465  1.166***  0.275  1.009***  0.268  1.199***  0.241  FRAG  −9.674**  4.521  −9.680***  3.093  −8.998***  3.334  −9.386***  2.878  FRAG_2  9.365**  4.358  9.342***  3.492  8.511**  3.569  8.983***  3.202  Additional covariates  A  A  A  A  Adjusted-R2  0.622  0.632  —  0.642  Observations  154  154  154  154  Instruments  Institutional & historical (1)  Institutional & historical (1)  Institutional & historical (1)  Institutional & historical (2)    Partial F  Adj.-R2  Partial F  Adj.-R2  —  —  Partial F  Adj.-R2  SAREA  29.12***  0.519  29.12***  0.519  —  —  42.24***  0.584  SAREA_2  58.57***  0.280  58.57***  0.280  —  —  30.52***  0.400  POP  59.37***  0.741      —  —      POP_2  189.17***  0.910      —  —      log(DENSITY)  7.52***  0.664  7.52***  0.664  —  —  7.60***  0.663  FRAG  9.27***  0.403  9.27***  0.403  —  —  9.43***  0.415  FRAG_2  5.40***  0.336  5.40***  0.336  —  —  5.48***  0.341  No. of excluded instruments  14  14  14  12  Wu–Hausman test  1.402  2.042*  —  2.302**  Sargan test  17.442**  17.785**  Hansen J-Test: 10.981*  18.637**    [5] IV (Lewbel-2SLS)   [6] IV (Lewbel-GMM-CUE)   [7] IV (2SLS)   [8] IV (2SLS)   Variable  Coef.  Std. Err.  Coef.  Std. Err.  Coef.  Std. Err.  Coef.  Std. Err.  SAREA  −0.251***  0.072  −0.248**  0.121  0.025  0.141  −0.141  0.107  SAREA_2  0.008**  0.003  −0.001  0.011  0.000  0.006  0.002  0.007  POP          −4.824  3.104      POP_2          2.118  1.688      log(DENSITY)  0.950***  0.266  0.947***  0.272  1.700***  0.325  1.371***  0.255  FRAG  −9.375***  2.655  −9.360***  2.832  −9.882***  2.397  −7.366***  2.201  FRAG_2  8.769***  2.919  8.815***  3.071  8.976***  2.396  7.078***  2.353  Additional covariates  A  A  A  B  Adjusted-R2  0.646    0.657    Observations  154  154  106  106  Instruments  Institutional & historical (3) + artificial instruments  Institutional & historical (3) + artificial instruments  Institutional & historical (4)  Institutional & historical (4)    Partial F  Adj.-R2  —  —  Partial F  Adj.-R2  Partial F  Adj.-R2  SAREA  47.40***  0.720  —  —  21.64***  0.513  21.64***  0.513  SAREA_2  124.62***  0.771  —  —  12.58***  0.215  12.58***  0.215  POP      —  —  34.35***  0.752      POP_2      —  —  333.94***  0.938      log(DENSITY)  7.25***  0.684  —  —  6.89***  0.699  6.89***  0.699  FRAG  8.48***  0.442  —  —  9.83***  0.477  9.83***  0.477  FRAG_2  6.62***  0.372  —  —  6.20***  0.415  6.20***  0.415  No. of excluded instruments  19  19  15  15  Wu–Hausman test  2.74**  —  0.809  0.829  Sargan test  23.07*  Hansen J-Test: 20.12  18.25**  21.66***    [5] IV (Lewbel-2SLS)   [6] IV (Lewbel-GMM-CUE)   [7] IV (2SLS)   [8] IV (2SLS)   Variable  Coef.  Std. Err.  Coef.  Std. Err.  Coef.  Std. Err.  Coef.  Std. Err.  SAREA  −0.251***  0.072  −0.248**  0.121  0.025  0.141  −0.141  0.107  SAREA_2  0.008**  0.003  −0.001  0.011  0.000  0.006  0.002  0.007  POP          −4.824  3.104      POP_2          2.118  1.688      log(DENSITY)  0.950***  0.266  0.947***  0.272  1.700***  0.325  1.371***  0.255  FRAG  −9.375***  2.655  −9.360***  2.832  −9.882***  2.397  −7.366***  2.201  FRAG_2  8.769***  2.919  8.815***  3.071  8.976***  2.396  7.078***  2.353  Additional covariates  A  A  A  B  Adjusted-R2  0.646    0.657    Observations  154  154  106  106  Instruments  Institutional & historical (3) + artificial instruments  Institutional & historical (3) + artificial instruments  Institutional & historical (4)  Institutional & historical (4)    Partial F  Adj.-R2  —  —  Partial F  Adj.-R2  Partial F  Adj.-R2  SAREA  47.40***  0.720  —  —  21.64***  0.513  21.64***  0.513  SAREA_2  124.62***  0.771  —  —  12.58***  0.215  12.58***  0.215  POP      —  —  34.35***  0.752      POP_2      —  —  333.94***  0.938      log(DENSITY)  7.25***  0.684  —  —  6.89***  0.699  6.89***  0.699  FRAG  8.48***  0.442  —  —  9.83***  0.477  9.83***  0.477  FRAG_2  6.62***  0.372  —  —  6.20***  0.415  6.20***  0.415  No. of excluded instruments  19  19  15  15  Wu–Hausman test  2.74**  —  0.809  0.829  Sargan test  23.07*  Hansen J-Test: 20.12  18.25**  21.66***  Note: Dependent variable: log(AGRIPROX). Robust standard-errors in parentheses. ***, **, *: significance at the 1%, 5% and 10% levels, respectively. A: a constant, regional dummies (W, S and E), income per inhabitant (GDP_CAP), agricultural productivity determinants (YWHEAT, RAIN, SUNSHINE, TEMPERATURE, MEDALT) and squared terms on GDP_CAP, SUNSHINE, TEMPERATURE, MEDALT. Institutional & historical (1): using institutional and Acemoglu et al. (for year 1800) instruments described in the text. Institutional & historical (2): using institutional and Acemoglu et al. (for for year 1400) instruments described in the text. Note: Dependent variable: log(AGRIPROX). Robust standard-errors in parentheses. ***, **, *: significance at the 1%, 5% and 10% levels respectively. A: a constant, regional dummies (W, S and E), income per inhabitant (GDP_CAP), agricultural productivity determinants (YWHEAT, RAIN, SUNSHINE, TEMPERATURE, MEDALT) and squared terms on GDP_CAP, SUNSHINE, TEMPERATURE, MEDALT. B: For model [8] YWHEAT, MEDALT and MEDALT_2 are replaced by covariates from Bosker et al. (see text for details). Institutional & historical (3) + artificial instruments: using institutional and Acemoglu et al. (for year 1400) instruments described in the text and Lewbel artificial instruments built on heteroscedasticity in the first stage. Institutional & historical (4): using institutional and Bosker et al. (for year 1400) instruments described in the text. Table 3 Instrumental variables estimates   [1] IV (2SLS)   [2] IV (2SLS)   [3] IV (GMM-CUE)   [4] IV (2SLS)   Variable  Coef.  Std. Err.  Coef.  Std. Err.  Coef.  Std. Err.  Coef.  Std. Err.  SAREA  −0.304  0.304  −0.295**  0.130  −0.131  0.161  −0.244*  0.142  SAREA_2  0.012  0.012  0.011  0.008  0.002  0.009  0.007  0.008  POP  0.295  3.772              POP_2  −0.455  1.899              log(DENSITY)  1.207**  0.465  1.166***  0.275  1.009***  0.268  1.199***  0.241  FRAG  −9.674**  4.521  −9.680***  3.093  −8.998***  3.334  −9.386***  2.878  FRAG_2  9.365**  4.358  9.342***  3.492  8.511**  3.569  8.983***  3.202  Additional covariates  A  A  A  A  Adjusted-R2  0.622  0.632  —  0.642  Observations  154  154  154  154  Instruments  Institutional & historical (1)  Institutional & historical (1)  Institutional & historical (1)  Institutional & historical (2)    Partial F  Adj.-R2  Partial F  Adj.-R2  —  —  Partial F  Adj.-R2  SAREA  29.12***  0.519  29.12***  0.519  —  —  42.24***  0.584  SAREA_2  58.57***  0.280  58.57***  0.280  —  —  30.52***  0.400  POP  59.37***  0.741      —  —      POP_2  189.17***  0.910      —  —      log(DENSITY)  7.52***  0.664  7.52***  0.664  —  —  7.60***  0.663  FRAG  9.27***  0.403  9.27***  0.403  —  —  9.43***  0.415  FRAG_2  5.40***  0.336  5.40***  0.336  —  —  5.48***  0.341  No. of excluded instruments  14  14  14  12  Wu–Hausman test  1.402  2.042*  —  2.302**  Sargan test  17.442**  17.785**  Hansen J-Test: 10.981*  18.637**    [1] IV (2SLS)   [2] IV (2SLS)   [3] IV (GMM-CUE)   [4] IV (2SLS)   Variable  Coef.  Std. Err.  Coef.  Std. Err.  Coef.  Std. Err.  Coef.  Std. Err.  SAREA  −0.304  0.304  −0.295**  0.130  −0.131  0.161  −0.244*  0.142  SAREA_2  0.012  0.012  0.011  0.008  0.002  0.009  0.007  0.008  POP  0.295  3.772              POP_2  −0.455  1.899              log(DENSITY)  1.207**  0.465  1.166***  0.275  1.009***  0.268  1.199***  0.241  FRAG  −9.674**  4.521  −9.680***  3.093  −8.998***  3.334  −9.386***  2.878  FRAG_2  9.365**  4.358  9.342***  3.492  8.511**  3.569  8.983***  3.202  Additional covariates  A  A  A  A  Adjusted-R2  0.622  0.632  —  0.642  Observations  154  154  154  154  Instruments  Institutional & historical (1)  Institutional & historical (1)  Institutional & historical (1)  Institutional & historical (2)    Partial F  Adj.-R2  Partial F  Adj.-R2  —  —  Partial F  Adj.-R2  SAREA  29.12***  0.519  29.12***  0.519  —  —  42.24***  0.584  SAREA_2  58.57***  0.280  58.57***  0.280  —  —  30.52***  0.400  POP  59.37***  0.741      —  —      POP_2  189.17***  0.910      —  —      log(DENSITY)  7.52***  0.664  7.52***  0.664  —  —  7.60***  0.663  FRAG  9.27***  0.403  9.27***  0.403  —  —  9.43***  0.415  FRAG_2  5.40***  0.336  5.40***  0.336  —  —  5.48***  0.341  No. of excluded instruments  14  14  14  12  Wu–Hausman test  1.402  2.042*  —  2.302**  Sargan test  17.442**  17.785**  Hansen J-Test: 10.981*  18.637**    [5] IV (Lewbel-2SLS)   [6] IV (Lewbel-GMM-CUE)   [7] IV (2SLS)   [8] IV (2SLS)   Variable  Coef.  Std. Err.  Coef.  Std. Err.  Coef.  Std. Err.  Coef.  Std. Err.  SAREA  −0.251***  0.072  −0.248**  0.121  0.025  0.141  −0.141  0.107  SAREA_2  0.008**  0.003  −0.001  0.011  0.000  0.006  0.002  0.007  POP          −4.824  3.104      POP_2          2.118  1.688      log(DENSITY)  0.950***  0.266  0.947***  0.272  1.700***  0.325  1.371***  0.255  FRAG  −9.375***  2.655  −9.360***  2.832  −9.882***  2.397  −7.366***  2.201  FRAG_2  8.769***  2.919  8.815***  3.071  8.976***  2.396  7.078***  2.353  Additional covariates  A  A  A  B  Adjusted-R2  0.646    0.657    Observations  154  154  106  106  Instruments  Institutional & historical (3) + artificial instruments  Institutional & historical (3) + artificial instruments  Institutional & historical (4)  Institutional & historical (4)    Partial F  Adj.-R2  —  —  Partial F  Adj.-R2  Partial F  Adj.-R2  SAREA  47.40***  0.720  —  —  21.64***  0.513  21.64***  0.513  SAREA_2  124.62***  0.771  —  —  12.58***  0.215  12.58***  0.215  POP      —  —  34.35***  0.752      POP_2      —  —  333.94***  0.938      log(DENSITY)  7.25***  0.684  —  —  6.89***  0.699  6.89***  0.699  FRAG  8.48***  0.442  —  —  9.83***  0.477  9.83***  0.477  FRAG_2  6.62***  0.372  —  —  6.20***  0.415  6.20***  0.415  No. of excluded instruments  19  19  15  15  Wu–Hausman test  2.74**  —  0.809  0.829  Sargan test  23.07*  Hansen J-Test: 20.12  18.25**  21.66***    [5] IV (Lewbel-2SLS)   [6] IV (Lewbel-GMM-CUE)   [7] IV (2SLS)   [8] IV (2SLS)   Variable  Coef.  Std. Err.  Coef.  Std. Err.  Coef.  Std. Err.  Coef.  Std. Err.  SAREA  −0.251***  0.072  −0.248**  0.121  0.025  0.141  −0.141  0.107  SAREA_2  0.008**  0.003  −0.001  0.011  0.000  0.006  0.002  0.007  POP          −4.824  3.104      POP_2          2.118  1.688      log(DENSITY)  0.950***  0.266  0.947***  0.272  1.700***  0.325  1.371***  0.255  FRAG  −9.375***  2.655  −9.360***  2.832  −9.882***  2.397  −7.366***  2.201  FRAG_2  8.769***  2.919  8.815***  3.071  8.976***  2.396  7.078***  2.353  Additional covariates  A  A  A  B  Adjusted-R2  0.646    0.657    Observations  154  154  106  106  Instruments  Institutional & historical (3) + artificial instruments  Institutional & historical (3) + artificial instruments  Institutional & historical (4)  Institutional & historical (4)    Partial F  Adj.-R2  —  —  Partial F  Adj.-R2  Partial F  Adj.-R2  SAREA  47.40***  0.720  —  —  21.64***  0.513  21.64***  0.513  SAREA_2  124.62***  0.771  —  —  12.58***  0.215  12.58***  0.215  POP      —  —  34.35***  0.752      POP_2      —  —  333.94***  0.938      log(DENSITY)  7.25***  0.684  —  —  6.89***  0.699  6.89***  0.699  FRAG  8.48***  0.442  —  —  9.83***  0.477  9.83***  0.477  FRAG_2  6.62***  0.372  —  —  6.20***  0.415  6.20***  0.415  No. of excluded instruments  19  19  15  15  Wu–Hausman test  2.74**  —  0.809  0.829  Sargan test  23.07*  Hansen J-Test: 20.12  18.25**  21.66***  Note: Dependent variable: log(AGRIPROX). Robust standard-errors in parentheses. ***, **, *: significance at the 1%, 5% and 10% levels, respectively. A: a constant, regional dummies (W, S and E), income per inhabitant (GDP_CAP), agricultural productivity determinants (YWHEAT, RAIN, SUNSHINE, TEMPERATURE, MEDALT) and squared terms on GDP_CAP, SUNSHINE, TEMPERATURE, MEDALT. Institutional & historical (1): using institutional and Acemoglu et al. (for year 1800) instruments described in the text. Institutional & historical (2): using institutional and Acemoglu et al. (for for year 1400) instruments described in the text. Note: Dependent variable: log(AGRIPROX). Robust standard-errors in parentheses. ***, **, *: significance at the 1%, 5% and 10% levels respectively. A: a constant, regional dummies (W, S and E), income per inhabitant (GDP_CAP), agricultural productivity determinants (YWHEAT, RAIN, SUNSHINE, TEMPERATURE, MEDALT) and squared terms on GDP_CAP, SUNSHINE, TEMPERATURE, MEDALT. B: For model [8] YWHEAT, MEDALT and MEDALT_2 are replaced by covariates from Bosker et al. (see text for details). Institutional & historical (3) + artificial instruments: using institutional and Acemoglu et al. (for year 1400) instruments described in the text and Lewbel artificial instruments built on heteroscedasticity in the first stage. Institutional & historical (4): using institutional and Bosker et al. (for year 1400) instruments described in the text. Table 4 Panel data estimates Panel A—dependent variable: GVA per worker     [1] Linear  [2] Linear  [3] Log-linear  [4] Log-linear  POP  −5960.007***  −6523.646***  −0.217***  −0.217***  (2085.482)  (1996.367)  (0.071)  (0.070)  POP_2  180.055**  182.041**  0.006**  0.006**  (88.800)  (80.897)  (0.003)  (0.003)  log(DENSITY)  —  11126.042***  —  0.042    (1926.419)    (0.064)  DENSITY  2697.290  —  0.014  —  (1931.881)    (0.074)    DENSITY _2  268.116  —  0.003  —  (280.009)    (0.011)    FRAG  −10246.459***  −11382.715***  −0.256***  −0.268***  (2626.592)  (2584.500)  (0.082)  (0.081)  FRAG_2  1836.180***  2210.350***  0.058***  0.061***  (612.100)  (594.933)  (0.020)  (0.020)  GDP_CAP  10858.356***  10433.578***  0.647***  0.621***  (3279.907)  (3356.435)  (0.096)  (0.094)  GDP_CAP  −938.586*  −904.933*  −0.075***  −0.072***  (511.803)  (518.286)  (0.014)  (0.014)  Adjusted-R2  0.172  0.168  0.276  0.275  Observations  930  930  930  930    Panel B—dependent variable: GVA per hectare     [5] Linear  [6] Linear  [7] Log-linear  [8] Log-linear    POP  −0.022**  −0.020**  −0.189***  −0.181**  (0.009)  (0.008)  (0.071)  (0.072)  POP_2  0.001  0.001  0.006**  0.006**  (0.001)  (0.001)  (0.003)  (0.003)  log(DENSITY)  —  −0.009  —  −0.052    (0.011)    (0.052)  DENSITY  −0.022  —  −0.056  —  (0.018)    (0.062)    DENSITY _2  0.003  —  0.008  —  (0.003)    (0.009)    FRAG  −0.025*  −0.026**  −0.174**  −0.179**  (0.013)  (0.013)  (0.073)  (0.072)  FRAG_2  0.005  0.006*  0.039**  0.040**  (0.003)  (0.003)  (0.018)  (0.017)  GDP_CAP  0.014  0.013  0.276***  0.261***  (0.018)  (0.018)  (0.088)  (0.087)  GDP_CAP  0.002  0.002  −0.021*  −0.019  (0.004)  (0.004)  (0.013)  (0.012)  Adjusted-R2  0.027  0.026  0.067  0.067  Observations  930  930  930  930  Panel A—dependent variable: GVA per worker     [1] Linear  [2] Linear  [3] Log-linear  [4] Log-linear  POP  −5960.007***  −6523.646***  −0.217***  −0.217***  (2085.482)  (1996.367)  (0.071)  (0.070)  POP_2  180.055**  182.041**  0.006**  0.006**  (88.800)  (80.897)  (0.003)  (0.003)  log(DENSITY)  —  11126.042***  —  0.042    (1926.419)    (0.064)  DENSITY  2697.290  —  0.014  —  (1931.881)    (0.074)    DENSITY _2  268.116  —  0.003  —  (280.009)    (0.011)    FRAG  −10246.459***  −11382.715***  −0.256***  −0.268***  (2626.592)  (2584.500)  (0.082)  (0.081)  FRAG_2  1836.180***  2210.350***  0.058***  0.061***  (612.100)  (594.933)  (0.020)  (0.020)  GDP_CAP  10858.356***  10433.578***  0.647***  0.621***  (3279.907)  (3356.435)  (0.096)  (0.094)  GDP_CAP  −938.586*  −904.933*  −0.075***  −0.072***  (511.803)  (518.286)  (0.014)  (0.014)  Adjusted-R2  0.172  0.168  0.276  0.275  Observations  930  930  930  930    Panel B—dependent variable: GVA per hectare     [5] Linear  [6] Linear  [7] Log-linear  [8] Log-linear    POP  −0.022**  −0.020**  −0.189***  −0.181**  (0.009)  (0.008)  (0.071)  (0.072)  POP_2  0.001  0.001  0.006**  0.006**  (0.001)  (0.001)  (0.003)  (0.003)  log(DENSITY)  —  −0.009  —  −0.052    (0.011)    (0.052)  DENSITY  −0.022  —  −0.056  —  (0.018)    (0.062)    DENSITY _2  0.003  —  0.008  —  (0.003)    (0.009)    FRAG  −0.025*  −0.026**  −0.174**  −0.179**  (0.013)  (0.013)  (0.073)  (0.072)  FRAG_2  0.005  0.006*  0.039**  0.040**  (0.003)  (0.003)  (0.018)  (0.017)  GDP_CAP  0.014  0.013  0.276***  0.261***  (0.018)  (0.018)  (0.088)  (0.087)  GDP_CAP  0.002  0.002  −0.021*  −0.019  (0.004)  (0.004)  (0.013)  (0.012)  Adjusted-R2  0.027  0.026  0.067  0.067  Observations  930  930  930  930  Note: Robust standard errors in parentheses. ***, **, *: significance at the 1%, 5% and 10% levels, respectively. TL3 regions and year fixed-effects are included but not reported here. Table 4 Panel data estimates Panel A—dependent variable: GVA per worker     [1] Linear  [2] Linear  [3] Log-linear  [4] Log-linear  POP  −5960.007***  −6523.646***  −0.217***  −0.217***  (2085.482)  (1996.367)  (0.071)  (0.070)  POP_2  180.055**  182.041**  0.006**  0.006**  (88.800)  (80.897)  (0.003)  (0.003)  log(DENSITY)  —  11126.042***  —  0.042    (1926.419)    (0.064)  DENSITY  2697.290  —  0.014  —  (1931.881)    (0.074)    DENSITY _2  268.116  —  0.003  —  (280.009)    (0.011)    FRAG  −10246.459***  −11382.715***  −0.256***  −0.268***  (2626.592)  (2584.500)  (0.082)  (0.081)  FRAG_2  1836.180***  2210.350***  0.058***  0.061***  (612.100)  (594.933)  (0.020)  (0.020)  GDP_CAP  10858.356***  10433.578***  0.647***  0.621***  (3279.907)  (3356.435)  (0.096)  (0.094)  GDP_CAP  −938.586*  −904.933*  −0.075***  −0.072***  (511.803)  (518.286)  (0.014)  (0.014)  Adjusted-R2  0.172  0.168  0.276  0.275  Observations  930  930  930  930    Panel B—dependent variable: GVA per hectare     [5] Linear  [6] Linear  [7] Log-linear  [8] Log-linear    POP  −0.022**  −0.020**  −0.189***  −0.181**  (0.009)  (0.008)  (0.071)  (0.072)  POP_2  0.001  0.001  0.006**  0.006**  (0.001)  (0.001)  (0.003)  (0.003)  log(DENSITY)  —  −0.009  —  −0.052    (0.011)    (0.052)  DENSITY  −0.022  —  −0.056  —  (0.018)    (0.062)    DENSITY _2  0.003  —  0.008  —  (0.003)    (0.009)    FRAG  −0.025*  −0.026**  −0.174**  −0.179**  (0.013)  (0.013)  (0.073)  (0.072)  FRAG_2  0.005  0.006*  0.039**  0.040**  (0.003)  (0.003)  (0.018)  (0.017)  GDP_CAP  0.014  0.013  0.276***  0.261***  (0.018)  (0.018)  (0.088)  (0.087)  GDP_CAP  0.002  0.002  −0.021*  −0.019  (0.004)  (0.004)  (0.013)  (0.012)  Adjusted-R2  0.027  0.026  0.067  0.067  Observations  930  930  930  930  Panel A—dependent variable: GVA per worker     [1] Linear  [2] Linear  [3] Log-linear  [4] Log-linear  POP  −5960.007***  −6523.646***  −0.217***  −0.217***  (2085.482)  (1996.367)  (0.071)  (0.070)  POP_2  180.055**  182.041**  0.006**  0.006**  (88.800)  (80.897)  (0.003)  (0.003)  log(DENSITY)  —  11126.042***  —  0.042    (1926.419)    (0.064)  DENSITY  2697.290  —  0.014  —  (1931.881)    (0.074)    DENSITY _2  268.116  —  0.003  —  (280.009)    (0.011)    FRAG  −10246.459***  −11382.715***  −0.256***  −0.268***  (2626.592)  (2584.500)  (0.082)  (0.081)  FRAG_2  1836.180***  2210.350***  0.058***  0.061***  (612.100)  (594.933)  (0.020)  (0.020)  GDP_CAP  10858.356***  10433.578***  0.647***  0.621***  (3279.907)  (3356.435)  (0.096)  (0.094)  GDP_CAP  −938.586*  −904.933*  −0.075***  −0.072***  (511.803)  (518.286)  (0.014)  (0.014)  Adjusted-R2  0.172  0.168  0.276  0.275  Observations  930  930  930  930    Panel B—dependent variable: GVA per hectare     [5] Linear  [6] Linear  [7] Log-linear  [8] Log-linear    POP  −0.022**  −0.020**  −0.189***  −0.181**  (0.009)  (0.008)  (0.071)  (0.072)  POP_2  0.001  0.001  0.006**  0.006**  (0.001)  (0.001)  (0.003)  (0.003)  log(DENSITY)  —  −0.009  —  −0.052    (0.011)    (0.052)  DENSITY  −0.022  —  −0.056  —  (0.018)    (0.062)    DENSITY _2  0.003  —  0.008  —  (0.003)    (0.009)    FRAG  −0.025*  −0.026**  −0.174**  −0.179**  (0.013)  (0.013)  (0.073)  (0.072)  FRAG_2  0.005  0.006*  0.039**  0.040**  (0.003)  (0.003)  (0.018)  (0.017)  GDP_CAP  0.014  0.013  0.276***  0.261***  (0.018)  (0.018)  (0.088)  (0.087)  GDP_CAP  0.002  0.002  −0.021*  −0.019  (0.004)  (0.004)  (0.013)  (0.012)  Adjusted-R2  0.027  0.026  0.067  0.067  Observations  930  930  930  930  Note: Robust standard errors in parentheses. ***, **, *: significance at the 1%, 5% and 10% levels, respectively. TL3 regions and year fixed-effects are included but not reported here. 6. Features of urban development and agricultural productivity The estimated models can be used to assess the impact of fragmentation and density on agricultural productivity. Using the estimates presented in this article, we can express agricultural productivity as a function of density and fragmentation:   π^=fDENSITY,FRAG,X¯, (3) where all other covariates are set at their sample mean X¯. Figure 2 presents iso-return curves in the plane of population density and fragmentation. Blue dots in Figure 2 represent cities included in the sample. Panel (a) is established based on model [4] presented in Table 2. Panels (b) and (c) are established based on IV models [1] and [8] in Table 3. Panel (d) represents the panel data model [2] from Table 4.23 For each panel, given the level of fragmentation, the iso-return curves show that agricultural productivity first increase and then decrease as population density increase. For example, in Panel (a) at fragmentation level 0.2, agricultural productivity increase from about $4000 to $11,000 as population density increases from 5000 inhabitants/km2 to 10,000 inhabitants/km2. Agricultural productivity reaches a maximum at approximately 15,000 inhabitants/km2 before decreasing as density increases. This decrease is not robust as described above with only six cities above this threshold. In other panels, based on models including log(DENSITY), increases in population density always leads to higher agricultural productivity. Figure 2 View largeDownload slide Iso-return curves in the plane of densification and fragmentation (OLS and IV models). Figure 2 View largeDownload slide Iso-return curves in the plane of densification and fragmentation (OLS and IV models). Agricultural productivity is especially sensitive to urban population density in highly fragmented urban areas or near compactly developed urban fringes. Is is relatively less sensitive to population density in urban areas with low or moderate fragmentation. The result that increasing population density increases agricultural productivity is consistent with our expectations based on theory. Increasing population density raises the demand for local produce, which will lead to higher prices and more land allocated to the local produce. In addition, because less land will be allocated to producing traded goods, the demand for input for traded goods will decrease, which will lead to a lower input price and higher per-acre profit for traded goods. This suggests that increasing population density will lead to higher per-acre profit for both local produce and trade goods. In contrast, given the population density, the iso-return curves show that agricultural productivity first decreases and then increases as fragmentation increases. The impact of fragmentation on agricultural productivity is reinforced by increasing population density. At low-population density levels, increased fragmentation barely affects agricultural productivity. However, as population density increases, the effect of fragmentation increases. In Panel (b) of Figure 2, holding population density at 10,000 inhabitants/km2, increasing fragmentation from 0.2 to 0.5 decreases agricultural productivity approximately from $12,000 to $5000. Further increase in fragmentation increases agricultural productivity; agricultural productivity increases approximately from $5000 to $10,000 as fragmentation increases from 0.6 to 0.8. The nonlinear relationship between fragmentation and agricultural productivity is also consistent with our expectations based on theory. Urban fragmentation may increase production costs and make it less profitable to switch from traditional crops to high-value crops. As a result, the output prices of high-value crops will be higher, while the input prices will be lower with increasing fragmentation. The effects of fragmentation on input and output prices of traditional crops will be the opposite. Thus, as fragmentation increases, the per-acre profit for high-value crops tends to increase, while the per-acre profits for traditional crops tends to decrease. At lower levels of fragmentation, the effect on traditional crops dominates the effect on high-value crops, leading to lower productivity as fragmentation increases. The opposite may be true at higher levels of fragmentation because more land is devoted to high-value crops with increasing urbanization and the effect on high-value crops may become dominate. 7. Policy implications Our empirical application suggests that, at least in Europe, increasing population density will improve per-hectare agricultural productivity at most urban fringes. Fragmentation also affects agricultural productivity, but in a nonlinear fashion. Increasing fragmentation reduces agricultural productivity initially. But when fragmentation reaches a certain threshold, further increases in fragmentation will increase agricultural productivity. Currently, less than half of European cities have reached this threshold. The nonlinear relationship between fragmentation and agricultural productivity suggests that different policy strategies should be adopted to protect farm income at the fringe of cities with different levels of fragmentation and population densities. Both the population densities and the level of fragmentation vary significantly across European cities.24 Cities in Northern and Western Europe tend to have low population densities and low fragmentation. In contrast, cities in Southern and Eastern Europe are much more heterogeneous in terms of population densities and spatial configurations. Our results suggest that for cities with low population densities and low fragmentation, such as those located in Northern Europe, anti-sprawl policies, for the benefits of farming, should concentrate on both density control and pattern management. In those cities, policies that encourage contiguous, dense development will increase agricultural productivity. In contrast, for cities with highly fragmented urban development patterns, such as many of those located in Eastern and Southern Europe, anti-sprawl policies, for the benefits of farming, should concentrate on density management. In those cities, further fragmentation could potentially increase agricultural productivity, particularly when the population density is also high.25 These results offer a renewed look at anti-sprawl policies, which are often justified for internalizing environmental impacts, traffic congestion and public services costs associated with urban development (Brueckner, 2001). In this article, we find that anti-sprawl policies can affect farm income by influencing population densities and development patterns. Although some studies have examined the effect of land use and urban growth control policies on total developed areas and population densities (see, e.g. Geshkov and DeSalvo, 2012), relatively few studies have examined their effects on fragmentation. Zoning may well be effective in controlling development inside the protected area, but may generate leapfrog development in the vicinity of the protected area (Irwin and Bockstael, 2004; Wu, 2006). This suggests that it may be difficult to control fragmentation. Fortunately, fragmentation does not significantly affect agricultural productivity when population density is low. When population densities are high and urban development is highly fragmented, further fragmentation will likely enhance agricultural productivity. This suggests that land-use policy for protecting farmland and farm income should be set primarily on the basis of their effectiveness for controlling the density of development, rather than patterns of development. 8. Conclusion This article constitutes a first attempt to assess the effects of two dimensions of urbanization, increasing population density and increasing urban fragmentation, on agricultural productivity in EU countries. We found that while increasing population density will increase agricultural productivity for most European cities, increasing urban fragmentation can have a positive or negative effect on agricultural productivity, depending on the population density and the existing level of urban fragmentation. Although most European cities are still below the threshold of population density, above which further increases in population density will lead to lower agricultural productivity, almost half of the European cities in our sample have already passed the fragmentation threshold, above which further increases in fragmentation will lead to higher agricultural productivity. Agricultural productivity is more sensitive to population density than to urban fragmentation, at least at low and medium density levels. Agricultural productivity becomes more sensitive to urban fragmentation as population density increases. These results are highly robust to alternative strategies to cope with model uncertainty and endogeneity of urban equilibrium covariates. Our results suggest that urban planning policies influencing population density and urban fragmentation can affect agricultural productivity and farm income. Specifically, policies that encourage compact development in a city may increase agricultural productivity and per-hectare farm net returns in the surrounding agricultural areas. In highly fragmented, low-density areas, land use policy should focus on increasing population density. This will not only reduce the negative externalities associated with urban sprawl, but will also increase agricultural productivity. However, literature on this subject is sparse, and further research is needed to fill the gap in the literature and to inform the design of policies targeted for urban growth management and rural development. Supplementary material Supplementary data for this paper are available at Journal of Economic Geography online. Acknowledgements The authors would like to thank Kristian Behrens and two anonymous reviewers for their insightful comments. Funding Walid Oueslati and Julien Salanié acknowledge funding from the European Union by the European Commission within the Seventh Framework Programme in the frame of RURAGRI ERA-NET under Grant Agreement no. 235175 TRUSTEE (ANR-13-RURA-0001-01). The authors only are responsible for any omissions or deficiencies. Neither the TRUSTEE project and any of its partner organizations, nor any organization of the European Union or European Commission are accountable for the content of this research. Footnotes 1 Please see Paül and McKenzie (2013), Pölling et al. (2016), or Wästfelt and Zhang (2016) for recent case studies on the structure and evolution of peri-urban farming in Europe. 2 The Urban Audit database arises from a project coordinated by Eurostat that aims to provide a wide range of indicators of socioeconomic and environmental issues. These indicators are measured across four periods: 1989–1993, 1994–1998, 1999–2002 and 2003–2006. For further details, refer to: http://epp.eurostat.ec.europa.eu/portal/page/portal/region_cities/city_urban. 3 ESPON is a European research program, which provides pan-European evidence and knowledge about European territorial structures, trends, perspectives and policy impacts that enable comparisons among regions and cities. For further details, see: http://database.espon.eu/. 4 These correlations are shown on our sample in Figure A1 of the Online Appendix. 5 Total population represents all residents who have their residence within the LUZ. 6 The Online Appendix lists the 208 cities included in our study and their geographical groupings. 7 We refer the reader to Tosics et al. (2010) for an in-depth description of these classes. 8 To build this instrument, we used the cities listed in the comprehensive survey on strategic bombings from Wikipedia (http://en.wikipedia.org/wiki/Strategic_bombing_during_World_War_II). 9 They do not cover Baltic countries. 10 TL3 Regions per country: Austria (35), Czech Republic (14), Estonia (5), Finland (19), France (94), Greece (13), Hungary (20), Ireland (8), Latvia (6), Poland (66), Slovakia (8), Slovenia (1), Sweden (21). 11 Measured, as in the preceding section, by the number of urban fragments over the total urbanized area. 12 Data, R scripts and results presented in this section and in the appendices are available in the Online Appendix. 13 We also tested the inclusion of an interaction term between FRAG and DENSITY. The effect is not consistently significant. In economic terms, it does not change our core results when significant. This interaction term would also be difficult to instrument so we preferred to present specifications without an interaction term. Table A3 in the Online Appendix reproduces Table 2 with an interaction term. The figure below Table A3 reproduces Figure 2 for a specification [A3.3] where the interaction term is significant. 14 Covariates selection is also consistent with that of bootstrapped stepwise selection (Austin and Tu, 2004) performed both ways using 1000 bootstrapped samples on the same set of candidate covariates. The model selected by bootstrapped stepwise corresponds to the best model identified by BMA. 15 We instrument squared terms to avoid the ‘forbidden regression’ pitfall well described in Angrist and Pischke (2008, 190–192) and Wooldridge (2010, 126–129 and 266–268). 16 While climate covariates determine urban land demand, soil quality and terrain features play on construction costs and aggregate urban land supply. 17 We have also tested specification with a proxy for the crop mix. Crop mix adjustments are one mechanism, through which urbanization affects agricultural productivity. Our core results hold with this additional control (Appendix 2 and Table A6 in the Online Appendix). 18 All first stage regressions are available in the Online Appendix. 19 Based on soil qualification maps. 20 Measured as the standard deviation of terrain elevation in a 10 km radius circle around each settlement. 21 The Bayesian Sargan tests correctly fail to reject our over-identifying exclusion restrictions. As suggested by Kass and Raftery (1995), there is evidence in favor of a theory when the posterior inclusion probability of the corresponding parameter is above 50%. Support is stronger for greater posterior inclusion probabilities. However, West et al. (2003) suggest that parameters with posterior inclusion probabilities above 30% are policy relevant. 22 In Table A5 of the Online Appendix, we give the variance decomposition of density, fragmentation, and the dependent variables. 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